Mean-Variance Hedging When There Are Jumps

Andrew E. B. Lim

78 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

Abstract

In this paper, we consider the problem of mean-variance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem, and closed form expressions for the optimal hedging policy are obtained using methods from stochastic control and the theory of backward stochastic differential equations. The results we have obtained show how backward stochastic differential equations can be used to obtain solutions to optimal investment and hedging problems when discontinuities in the underlying price processes are modeled by the arrivals of Poisson processes with stochastic intensities. Applications to the problem of hedging default risk are also discussed.

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References

2007Brownian Motion and Stochastic Calculus 2003Financial Modelling with Jump Processes 1993Dynamic Asset Pricing Theory.2002A Jump-Diffusion Model for Option Pricing 2003The Impact of Jumps in Volatility and Returns 2000Post-'87 crash fears in the S&P 500 futures option market 1998On cox processes and credit risky securities 1979Calcul Stochastique et Problèmes de Martingales

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