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

Author

Listed:
  • Oleksandra Putyatina

    (University of Kaiserslautern)

  • Jörn Sass

    (University of Kaiserslautern)

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.

Suggested Citation

  • Oleksandra Putyatina & Jörn Sass, 2018. "Approximation for portfolio optimization in a financial market with shot-noise jumps," Computational Management Science, Springer, vol. 15(2), pages 161-186, June.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:2:d:10.1007_s10287-017-0294-5
    DOI: 10.1007/s10287-017-0294-5
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    References listed on IDEAS

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