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Approximation for portfolio optimization in a financial market with shot-noise jumps

Oleksandra Putyatina () and Jörn Sass ()
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Oleksandra Putyatina: University of Kaiserslautern
Jörn Sass: University of Kaiserslautern

Computational Management Science, 2018, vol. 15, issue 2, 161-186

Abstract: Abstract For an investor in a continuous-time financial market the portfolio optimization problem of maximizing expected utility of terminal wealth is considered. Stock prices are driven by a Brownian motion and a shot-noise process. The latter leads to jumps in the stock prices whose influence decays exponentially with time. We analyze this model using a stochastic control approach based on the Hamilton–Jacobi–Bellman (HJB) equation. Special cases are discussed motivating that an explicit solution is difficult. Two approximations are derived. Firstly, an approximation in the HJB equation using a Taylor expansion. Secondly, a Gaussian approximation of the shot noise process which leads to an explicit solution for the trading strategy. These approximations are compared in a simulation study with different strategies showing that for a wide range of model parameters the derived approximate strategies have a good performance.

Keywords: Utility maximization; HJB equation; Compound Poisson process; Gaussian approximation; Merton problem (search for similar items in EconPapers)
Date: 2018
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