Partial hedging in a stochastic volatility environment. (English) Zbl 1049.91073
In the paper the problem of partial hedging of a derivative security risk is considered as a problem to maximize a state dependent utility function. The Legendre transform is applied to corresponding Bellman partial differential equations in models with constant, time-dependent and stochastic volatility. Under the assumption that the volatility is fast mean reversing, two hedging strategies are constructed by using a single perturbation analysis, that are robust with respect to specification of a stochastic volatility model. Effectiveness of these strategies is studied numerically.
Reviewer: Zuzana Prášková (Praha)
MSC:
| 91B28 | Finance etc. (MSC2000) |
| 90C39 | Dynamic programming |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 91B70 | Stochastic models in economics |
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