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Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
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Applications of Malliavin calculus to Monte Carlo methods in finance
TLDR
An original probabilistic method for the numerical computations of Greeks in finance, based on the Greeks formulae, which is compared to the Monte Carlo finite difference approach and turns out to be very efficient in the case of discontinuous payoff functionals.
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Law Invariant Risk Measures Have the Fatou Property
S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterizationof law invariant coherent risk measures, satisfying the Fatou property.The latter property was introduced by F. Delbaen [D 02].…
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Weak Dynamic Programming Principle for Viscosity Solutions
We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the…
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Wellposedness of second order backward SDEs
We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order…
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Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE
Preface.- 1. Conditional Expectation and Linear Parabolic PDEs.- 2. Stochastic Control and Dynamic Programming.- 3. Optimal Stopping and Dynamic Programming.- 4. Solving Control Problems by…
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OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS
The connection between optimal stopping of random systems and the theory of the Snell envelop is well understood, and its application to the pricing of American contingent claims is well known.…
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Contingent Claims and Market Completeness in a Stochastic Volatility Model
In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in…
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OPTIMAL RISK SHARING FOR LAW INVARIANT MONETARY UTILITY FUNCTIONS
We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law‐invariant monetary utility functions or equivalently, law‐invariant risk…
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Option Hedging And Implied Volatilities In A Stochastic Volatility Model
In the stochastic volatility framework of Hull and White (1987), we characterize the so-called Black and Scholes implied volatility as a function of two arguments the ratio of the strike to the…
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