From Probability to Finance: Lecture Notes of BICMR Summer School on Financial Mathematics
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| Format: | Electronic eBook |
| Language: | English |
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Singapore
Springer Singapore Pte. Limited
2020
|
| Series: | Mathematical Lectures from Peking University Ser
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| Subjects: | |
| Item Description: | Description based on publisher supplied metadata and other sources |
| Physical Description: | 1 Online-Ressource (253 pages) |
| ISBN: | 9789811515767 |
Staff View
MARC
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| 245 | 1 | 0 | |a From Probability to Finance |b Lecture Notes of BICMR Summer School on Financial Mathematics |
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| 505 | 8 | |a Intro -- Preface -- Contents -- Continuous-State Branching Processes with Immigration -- 1 Laplace Transforms of Measures -- 2 Construction of CB-Processes -- 3 Some Basic Properties -- 4 Positive Integral Functionals -- 5 Construction of CBI-Processes -- 6 Structures of Sample Paths -- 7 Martingale Problem Formulations -- 8 Stochastic Equations for CBI-Processes -- 9 Local and Global Maximal Jumps -- 10 A Coupling of CBI-Processes -- References -- Enlargement of Filtration in Discrete Time -- 1 Some Well-Known Results and Definitions -- 1.1 Basic Definitions -- 1.2 mathbbH-Martingales -- 1.3 Doob's Decomposition and Applications -- 1.4 Projections -- 1.5 Multiplicative Decomposition -- 1.6 Stochastic Exponential Process -- 1.7 Stopping Times and Local Martingales -- 1.8 Change of Probability -- 1.9 Some Facts on Finance -- 1.10 Enlargement of Filtration -- 2 Initial Enlargement -- 2.1 Bridge -- 2.2 Viability -- 2.3 Initial Enlargement with a mathbbZ-Valued Random Variable ξ -- 2.4 Example: Supremum of a Random Walk -- 3 Introduction to Progressive Enlargement -- 3.1 General Results -- 3.2 Immersion in Progressive Enlargement -- 4 Progressive Enlargement Before τ -- 4.1 Semimartingale Decomposition -- 4.2 Viability -- 5 Progressive Enlargement After τ -- 5.1 General Case -- 5.2 Honest Times -- 5.3 Viability -- 6 Pseudo-Stopping Times -- 7 An Optional Representation for Martingales in a Progressive Enlargement -- 8 Other Enlargements -- 8.1 Enlargement with a Pair (ζ,τ) -- 8.2 Enlargement with a Process -- 9 Credit Risk -- References -- Clustering Effects via Hawkes Processes -- 1 Introduction -- 2 Point Processes: An Overview -- 2.1 What is a Point Processes? -- 2.2 Compensator and Intensity -- 2.3 The Poisson Process -- 2.4 Change of Probability -- 3 Hawkes Processes -- 3.1 A Time Change Approach to Hawkes Process | |
| 505 | 8 | |a 3.2 A Change of Probability Approach of the Hawkes Process -- 3.3 Maximum Likelihood Estimation -- 3.4 Limit Behaviour -- 4 Moments -- 4.1 Moments of the Intensity -- 4.2 Recurrence Formulae for Moments -- 5 Generalization of Hawkes Processes -- 5.1 Marked Hawkes Processes -- 5.2 Nonlinear Hawkes Processes -- 6 Financial Applications of Hawkes Processes -- 6.1 Calibration of Hawkes Processes -- 6.2 Interest Rate Model with Hawkes Jumps -- 6.3 Hawkes Processes for Credit Modelling -- 6.4 Clustering for Trading Orders and Optimal Execution -- 7 A Branching Processes Point of View -- 7.1 Branching Property and Integral Representation -- 7.2 Hawkes Processes and CBI Processes -- 7.3 Extensions -- References -- Bernstein Copulas and Composite Bernstein Copulas -- 1 Introduction -- 2 Bernstein Copulas -- 2.1 Definition of Bernstein Copulas -- 2.2 The BC Generated by a Copula Function -- 2.3 Convergence of Bernstein Copulas -- 2.4 The Density Function of the BC -- 2.5 Dependence Measures -- 2.6 Baker's Distribution-One Family of Distributions with BCs -- 2.7 Random Numbers Generation -- 3 Composite Bernstein Copula -- 3.1 Definition of Composite Bernstein Copula -- 3.2 Properties of the Composite Bernstein Copula -- 3.3 Reproduction Property -- 3.4 Bivariate Tail Dependence -- 3.5 Probabilistic Expressions for the CBC -- 3.6 The Simulation Method for CBC -- 3.7 Some Families of the CBC -- 4 Simulation Study and Stock Data Analysis -- 4.1 A Simulation Study -- 4.2 Stock Data Analysis -- 5 Conclusions -- References -- Wealth Transfers, Indifference Pricing, and XVA Compression Schemes -- 1 Introduction -- 1.1 Abbreviations -- 2 XVA Framework -- 2.1 Agents -- 2.2 Cash Flows -- 2.3 Valuation Operator -- 2.4 Contra-Assets and Contra-Liabilities -- 2.5 Cost of Capital -- 2.6 Funds Transfer Price -- 2.7 A General Result | |
| 505 | 8 | |a 3 Wealth Transfers Triggered by Market Incompleteness -- 3.1 The Limiting Case of Complete Markets -- 3.2 DVA Wealth Transfer Triggered by Shareholders Not Being Able to Redeem Bank Debt -- 3.3 CVACL Wealth Transfer Triggered by Shareholders Bankruptcy Costs -- 3.4 FVA Wealth Transfer Triggered by the Impossibility to REPO Derivatives -- 3.5 MVA Wealth Transfer Triggered by Different Funding Policies for Initial Margins -- 3.6 KVA Wealth Transfer Triggered by The Cost of Capital Which Is Required by the Impossibility of Hedging out Counterparty Default Losses -- 4 XVA Formulas and Wealth Transfers in a Static Setup -- 4.1 Cash Flows -- 4.2 Static XVA Formulas -- 5 Derivative Management: From Hedging to XVA Compression -- 5.1 Capital/Collateral Optimisation of Inter-Dealer Trades -- 5.2 Optimal Liquidation of the CCP Portfolio of a Defaulted Clearing Member -- 5.3 XVA Compression Cycles -- References | |
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| author | Jiao, Ying |
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| contents | Intro -- Preface -- Contents -- Continuous-State Branching Processes with Immigration -- 1 Laplace Transforms of Measures -- 2 Construction of CB-Processes -- 3 Some Basic Properties -- 4 Positive Integral Functionals -- 5 Construction of CBI-Processes -- 6 Structures of Sample Paths -- 7 Martingale Problem Formulations -- 8 Stochastic Equations for CBI-Processes -- 9 Local and Global Maximal Jumps -- 10 A Coupling of CBI-Processes -- References -- Enlargement of Filtration in Discrete Time -- 1 Some Well-Known Results and Definitions -- 1.1 Basic Definitions -- 1.2 mathbbH-Martingales -- 1.3 Doob's Decomposition and Applications -- 1.4 Projections -- 1.5 Multiplicative Decomposition -- 1.6 Stochastic Exponential Process -- 1.7 Stopping Times and Local Martingales -- 1.8 Change of Probability -- 1.9 Some Facts on Finance -- 1.10 Enlargement of Filtration -- 2 Initial Enlargement -- 2.1 Bridge -- 2.2 Viability -- 2.3 Initial Enlargement with a mathbbZ-Valued Random Variable ξ -- 2.4 Example: Supremum of a Random Walk -- 3 Introduction to Progressive Enlargement -- 3.1 General Results -- 3.2 Immersion in Progressive Enlargement -- 4 Progressive Enlargement Before τ -- 4.1 Semimartingale Decomposition -- 4.2 Viability -- 5 Progressive Enlargement After τ -- 5.1 General Case -- 5.2 Honest Times -- 5.3 Viability -- 6 Pseudo-Stopping Times -- 7 An Optional Representation for Martingales in a Progressive Enlargement -- 8 Other Enlargements -- 8.1 Enlargement with a Pair (ζ,τ) -- 8.2 Enlargement with a Process -- 9 Credit Risk -- References -- Clustering Effects via Hawkes Processes -- 1 Introduction -- 2 Point Processes: An Overview -- 2.1 What is a Point Processes? -- 2.2 Compensator and Intensity -- 2.3 The Poisson Process -- 2.4 Change of Probability -- 3 Hawkes Processes -- 3.1 A Time Change Approach to Hawkes Process 3.2 A Change of Probability Approach of the Hawkes Process -- 3.3 Maximum Likelihood Estimation -- 3.4 Limit Behaviour -- 4 Moments -- 4.1 Moments of the Intensity -- 4.2 Recurrence Formulae for Moments -- 5 Generalization of Hawkes Processes -- 5.1 Marked Hawkes Processes -- 5.2 Nonlinear Hawkes Processes -- 6 Financial Applications of Hawkes Processes -- 6.1 Calibration of Hawkes Processes -- 6.2 Interest Rate Model with Hawkes Jumps -- 6.3 Hawkes Processes for Credit Modelling -- 6.4 Clustering for Trading Orders and Optimal Execution -- 7 A Branching Processes Point of View -- 7.1 Branching Property and Integral Representation -- 7.2 Hawkes Processes and CBI Processes -- 7.3 Extensions -- References -- Bernstein Copulas and Composite Bernstein Copulas -- 1 Introduction -- 2 Bernstein Copulas -- 2.1 Definition of Bernstein Copulas -- 2.2 The BC Generated by a Copula Function -- 2.3 Convergence of Bernstein Copulas -- 2.4 The Density Function of the BC -- 2.5 Dependence Measures -- 2.6 Baker's Distribution-One Family of Distributions with BCs -- 2.7 Random Numbers Generation -- 3 Composite Bernstein Copula -- 3.1 Definition of Composite Bernstein Copula -- 3.2 Properties of the Composite Bernstein Copula -- 3.3 Reproduction Property -- 3.4 Bivariate Tail Dependence -- 3.5 Probabilistic Expressions for the CBC -- 3.6 The Simulation Method for CBC -- 3.7 Some Families of the CBC -- 4 Simulation Study and Stock Data Analysis -- 4.1 A Simulation Study -- 4.2 Stock Data Analysis -- 5 Conclusions -- References -- Wealth Transfers, Indifference Pricing, and XVA Compression Schemes -- 1 Introduction -- 1.1 Abbreviations -- 2 XVA Framework -- 2.1 Agents -- 2.2 Cash Flows -- 2.3 Valuation Operator -- 2.4 Contra-Assets and Contra-Liabilities -- 2.5 Cost of Capital -- 2.6 Funds Transfer Price -- 2.7 A General Result 3 Wealth Transfers Triggered by Market Incompleteness -- 3.1 The Limiting Case of Complete Markets -- 3.2 DVA Wealth Transfer Triggered by Shareholders Not Being Able to Redeem Bank Debt -- 3.3 CVACL Wealth Transfer Triggered by Shareholders Bankruptcy Costs -- 3.4 FVA Wealth Transfer Triggered by the Impossibility to REPO Derivatives -- 3.5 MVA Wealth Transfer Triggered by Different Funding Policies for Initial Margins -- 3.6 KVA Wealth Transfer Triggered by The Cost of Capital Which Is Required by the Impossibility of Hedging out Counterparty Default Losses -- 4 XVA Formulas and Wealth Transfers in a Static Setup -- 4.1 Cash Flows -- 4.2 Static XVA Formulas -- 5 Derivative Management: From Hedging to XVA Compression -- 5.1 Capital/Collateral Optimisation of Inter-Dealer Trades -- 5.2 Optimal Liquidation of the CCP Portfolio of a Defaulted Clearing Member -- 5.3 XVA Compression Cycles -- References |
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| dewey-full | 332.0151922 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
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| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
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| index_date | 2024-07-03T19:50:37Z |
| indexdate | 2024-07-10T09:32:26Z |
| institution | BVB |
| isbn | 9789811515767 |
| language | English |
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| series2 | Mathematical Lectures from Peking University Ser |
| spelling | Jiao, Ying Verfasser aut From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics Singapore Springer Singapore Pte. Limited 2020 ©2020 1 Online-Ressource (253 pages) txt rdacontent c rdamedia cr rdacarrier Mathematical Lectures from Peking University Ser Description based on publisher supplied metadata and other sources Intro -- Preface -- Contents -- Continuous-State Branching Processes with Immigration -- 1 Laplace Transforms of Measures -- 2 Construction of CB-Processes -- 3 Some Basic Properties -- 4 Positive Integral Functionals -- 5 Construction of CBI-Processes -- 6 Structures of Sample Paths -- 7 Martingale Problem Formulations -- 8 Stochastic Equations for CBI-Processes -- 9 Local and Global Maximal Jumps -- 10 A Coupling of CBI-Processes -- References -- Enlargement of Filtration in Discrete Time -- 1 Some Well-Known Results and Definitions -- 1.1 Basic Definitions -- 1.2 mathbbH-Martingales -- 1.3 Doob's Decomposition and Applications -- 1.4 Projections -- 1.5 Multiplicative Decomposition -- 1.6 Stochastic Exponential Process -- 1.7 Stopping Times and Local Martingales -- 1.8 Change of Probability -- 1.9 Some Facts on Finance -- 1.10 Enlargement of Filtration -- 2 Initial Enlargement -- 2.1 Bridge -- 2.2 Viability -- 2.3 Initial Enlargement with a mathbbZ-Valued Random Variable ξ -- 2.4 Example: Supremum of a Random Walk -- 3 Introduction to Progressive Enlargement -- 3.1 General Results -- 3.2 Immersion in Progressive Enlargement -- 4 Progressive Enlargement Before τ -- 4.1 Semimartingale Decomposition -- 4.2 Viability -- 5 Progressive Enlargement After τ -- 5.1 General Case -- 5.2 Honest Times -- 5.3 Viability -- 6 Pseudo-Stopping Times -- 7 An Optional Representation for Martingales in a Progressive Enlargement -- 8 Other Enlargements -- 8.1 Enlargement with a Pair (ζ,τ) -- 8.2 Enlargement with a Process -- 9 Credit Risk -- References -- Clustering Effects via Hawkes Processes -- 1 Introduction -- 2 Point Processes: An Overview -- 2.1 What is a Point Processes? -- 2.2 Compensator and Intensity -- 2.3 The Poisson Process -- 2.4 Change of Probability -- 3 Hawkes Processes -- 3.1 A Time Change Approach to Hawkes Process 3.2 A Change of Probability Approach of the Hawkes Process -- 3.3 Maximum Likelihood Estimation -- 3.4 Limit Behaviour -- 4 Moments -- 4.1 Moments of the Intensity -- 4.2 Recurrence Formulae for Moments -- 5 Generalization of Hawkes Processes -- 5.1 Marked Hawkes Processes -- 5.2 Nonlinear Hawkes Processes -- 6 Financial Applications of Hawkes Processes -- 6.1 Calibration of Hawkes Processes -- 6.2 Interest Rate Model with Hawkes Jumps -- 6.3 Hawkes Processes for Credit Modelling -- 6.4 Clustering for Trading Orders and Optimal Execution -- 7 A Branching Processes Point of View -- 7.1 Branching Property and Integral Representation -- 7.2 Hawkes Processes and CBI Processes -- 7.3 Extensions -- References -- Bernstein Copulas and Composite Bernstein Copulas -- 1 Introduction -- 2 Bernstein Copulas -- 2.1 Definition of Bernstein Copulas -- 2.2 The BC Generated by a Copula Function -- 2.3 Convergence of Bernstein Copulas -- 2.4 The Density Function of the BC -- 2.5 Dependence Measures -- 2.6 Baker's Distribution-One Family of Distributions with BCs -- 2.7 Random Numbers Generation -- 3 Composite Bernstein Copula -- 3.1 Definition of Composite Bernstein Copula -- 3.2 Properties of the Composite Bernstein Copula -- 3.3 Reproduction Property -- 3.4 Bivariate Tail Dependence -- 3.5 Probabilistic Expressions for the CBC -- 3.6 The Simulation Method for CBC -- 3.7 Some Families of the CBC -- 4 Simulation Study and Stock Data Analysis -- 4.1 A Simulation Study -- 4.2 Stock Data Analysis -- 5 Conclusions -- References -- Wealth Transfers, Indifference Pricing, and XVA Compression Schemes -- 1 Introduction -- 1.1 Abbreviations -- 2 XVA Framework -- 2.1 Agents -- 2.2 Cash Flows -- 2.3 Valuation Operator -- 2.4 Contra-Assets and Contra-Liabilities -- 2.5 Cost of Capital -- 2.6 Funds Transfer Price -- 2.7 A General Result 3 Wealth Transfers Triggered by Market Incompleteness -- 3.1 The Limiting Case of Complete Markets -- 3.2 DVA Wealth Transfer Triggered by Shareholders Not Being Able to Redeem Bank Debt -- 3.3 CVACL Wealth Transfer Triggered by Shareholders Bankruptcy Costs -- 3.4 FVA Wealth Transfer Triggered by the Impossibility to REPO Derivatives -- 3.5 MVA Wealth Transfer Triggered by Different Funding Policies for Initial Margins -- 3.6 KVA Wealth Transfer Triggered by The Cost of Capital Which Is Required by the Impossibility of Hedging out Counterparty Default Losses -- 4 XVA Formulas and Wealth Transfers in a Static Setup -- 4.1 Cash Flows -- 4.2 Static XVA Formulas -- 5 Derivative Management: From Hedging to XVA Compression -- 5.1 Capital/Collateral Optimisation of Inter-Dealer Trades -- 5.2 Optimal Liquidation of the CCP Portfolio of a Defaulted Clearing Member -- 5.3 XVA Compression Cycles -- References Business mathematics-Congresses (DE-588)4143413-4 Aufsatzsammlung gnd-content Erscheint auch als Druck-Ausgabe Jiao, Ying From Probability to Finance Singapore : Springer Singapore Pte. Limited,c2020 9789811515750 |
| spellingShingle | Jiao, Ying From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics Intro -- Preface -- Contents -- Continuous-State Branching Processes with Immigration -- 1 Laplace Transforms of Measures -- 2 Construction of CB-Processes -- 3 Some Basic Properties -- 4 Positive Integral Functionals -- 5 Construction of CBI-Processes -- 6 Structures of Sample Paths -- 7 Martingale Problem Formulations -- 8 Stochastic Equations for CBI-Processes -- 9 Local and Global Maximal Jumps -- 10 A Coupling of CBI-Processes -- References -- Enlargement of Filtration in Discrete Time -- 1 Some Well-Known Results and Definitions -- 1.1 Basic Definitions -- 1.2 mathbbH-Martingales -- 1.3 Doob's Decomposition and Applications -- 1.4 Projections -- 1.5 Multiplicative Decomposition -- 1.6 Stochastic Exponential Process -- 1.7 Stopping Times and Local Martingales -- 1.8 Change of Probability -- 1.9 Some Facts on Finance -- 1.10 Enlargement of Filtration -- 2 Initial Enlargement -- 2.1 Bridge -- 2.2 Viability -- 2.3 Initial Enlargement with a mathbbZ-Valued Random Variable ξ -- 2.4 Example: Supremum of a Random Walk -- 3 Introduction to Progressive Enlargement -- 3.1 General Results -- 3.2 Immersion in Progressive Enlargement -- 4 Progressive Enlargement Before τ -- 4.1 Semimartingale Decomposition -- 4.2 Viability -- 5 Progressive Enlargement After τ -- 5.1 General Case -- 5.2 Honest Times -- 5.3 Viability -- 6 Pseudo-Stopping Times -- 7 An Optional Representation for Martingales in a Progressive Enlargement -- 8 Other Enlargements -- 8.1 Enlargement with a Pair (ζ,τ) -- 8.2 Enlargement with a Process -- 9 Credit Risk -- References -- Clustering Effects via Hawkes Processes -- 1 Introduction -- 2 Point Processes: An Overview -- 2.1 What is a Point Processes? -- 2.2 Compensator and Intensity -- 2.3 The Poisson Process -- 2.4 Change of Probability -- 3 Hawkes Processes -- 3.1 A Time Change Approach to Hawkes Process 3.2 A Change of Probability Approach of the Hawkes Process -- 3.3 Maximum Likelihood Estimation -- 3.4 Limit Behaviour -- 4 Moments -- 4.1 Moments of the Intensity -- 4.2 Recurrence Formulae for Moments -- 5 Generalization of Hawkes Processes -- 5.1 Marked Hawkes Processes -- 5.2 Nonlinear Hawkes Processes -- 6 Financial Applications of Hawkes Processes -- 6.1 Calibration of Hawkes Processes -- 6.2 Interest Rate Model with Hawkes Jumps -- 6.3 Hawkes Processes for Credit Modelling -- 6.4 Clustering for Trading Orders and Optimal Execution -- 7 A Branching Processes Point of View -- 7.1 Branching Property and Integral Representation -- 7.2 Hawkes Processes and CBI Processes -- 7.3 Extensions -- References -- Bernstein Copulas and Composite Bernstein Copulas -- 1 Introduction -- 2 Bernstein Copulas -- 2.1 Definition of Bernstein Copulas -- 2.2 The BC Generated by a Copula Function -- 2.3 Convergence of Bernstein Copulas -- 2.4 The Density Function of the BC -- 2.5 Dependence Measures -- 2.6 Baker's Distribution-One Family of Distributions with BCs -- 2.7 Random Numbers Generation -- 3 Composite Bernstein Copula -- 3.1 Definition of Composite Bernstein Copula -- 3.2 Properties of the Composite Bernstein Copula -- 3.3 Reproduction Property -- 3.4 Bivariate Tail Dependence -- 3.5 Probabilistic Expressions for the CBC -- 3.6 The Simulation Method for CBC -- 3.7 Some Families of the CBC -- 4 Simulation Study and Stock Data Analysis -- 4.1 A Simulation Study -- 4.2 Stock Data Analysis -- 5 Conclusions -- References -- Wealth Transfers, Indifference Pricing, and XVA Compression Schemes -- 1 Introduction -- 1.1 Abbreviations -- 2 XVA Framework -- 2.1 Agents -- 2.2 Cash Flows -- 2.3 Valuation Operator -- 2.4 Contra-Assets and Contra-Liabilities -- 2.5 Cost of Capital -- 2.6 Funds Transfer Price -- 2.7 A General Result 3 Wealth Transfers Triggered by Market Incompleteness -- 3.1 The Limiting Case of Complete Markets -- 3.2 DVA Wealth Transfer Triggered by Shareholders Not Being Able to Redeem Bank Debt -- 3.3 CVACL Wealth Transfer Triggered by Shareholders Bankruptcy Costs -- 3.4 FVA Wealth Transfer Triggered by the Impossibility to REPO Derivatives -- 3.5 MVA Wealth Transfer Triggered by Different Funding Policies for Initial Margins -- 3.6 KVA Wealth Transfer Triggered by The Cost of Capital Which Is Required by the Impossibility of Hedging out Counterparty Default Losses -- 4 XVA Formulas and Wealth Transfers in a Static Setup -- 4.1 Cash Flows -- 4.2 Static XVA Formulas -- 5 Derivative Management: From Hedging to XVA Compression -- 5.1 Capital/Collateral Optimisation of Inter-Dealer Trades -- 5.2 Optimal Liquidation of the CCP Portfolio of a Defaulted Clearing Member -- 5.3 XVA Compression Cycles -- References Business mathematics-Congresses |
| subject_GND | (DE-588)4143413-4 |
| title | From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics |
| title_auth | From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics |
| title_exact_search | From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics |
| title_exact_search_txtP | From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics |
| title_full | From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics |
| title_fullStr | From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics |
| title_full_unstemmed | From Probability to Finance Lecture Notes of BICMR Summer School on Financial Mathematics |
| title_short | From Probability to Finance |
| title_sort | from probability to finance lecture notes of bicmr summer school on financial mathematics |
| title_sub | Lecture Notes of BICMR Summer School on Financial Mathematics |
| topic | Business mathematics-Congresses |
| topic_facet | Business mathematics-Congresses Aufsatzsammlung |
| work_keys_str_mv | AT jiaoying fromprobabilitytofinancelecturenotesofbicmrsummerschoolonfinancialmathematics |