Journal ArticleDOI
Backward Stochastic Differential Equations in Finance
TLDR
In this article, different properties of backward stochastic differential equations and their applications to finance are discussed. But the main focus of this paper is on the theory of contingent claim valuation, especially cases with constraints.Abstract:
We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b).read more
Citations
More filters
Book
Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
Journal ArticleDOI
Solving high-dimensional partial differential equations using deep learning
TL;DR: A deep learning-based approach that can handle general high-dimensional parabolic PDEs using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function.
Journal ArticleDOI
Backward stochastic differential equations and partial differential equations with quadratic growth
TL;DR: In this paper, the authors provide existence, comparison and stability results for one-dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) $F(t,Y, Z)$ is continuous and has a quadratic growth in $Z$ and the terminal condition is bounded.
Journal ArticleDOI
Ambiguity, risk, and asset returns in continuous time
Zengjing Chen,Larry G. Epstein +1 more
TL;DR: In this article, a continuous-time intertemporal version of multiple-priors utility, where aversion to ambiguity is admissible, is presented. But the model is restricted to a representative agent asset market setting.
Posted Content
Ambiguity, risk and asset returns in continuous time
Zengjing Chen,Larry G. Epstein +1 more
TL;DR: In this article, a continuous-time intertemporal version of multiple-priors utility, where aversion to ambiguity is admissible, is proposed for a representative agent asset market setting, which delivers restrictions on excess returns that admit interpretations reflecting a premium for risk and a separate premium for ambiguity.
References
More filters
Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Book
Theory of rational option pricing
TL;DR: In this paper, the authors deduced a set of restrictions on option pricing formulas from the assumption that investors prefer more to less, which are necessary conditions for a formula to be consistent with a rational pricing theory.
Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
Journal ArticleDOI
Optimum consumption and portfolio rules in a continuous-time model☆
TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.
Related Papers (5)
Adapted solution of a backward stochastic differential equation
Backward stochastic differential equations and quasilinear parabolic partial differential equations
Etienne Pardoux,Shige Peng +1 more