A martingale approach for asset allocation with derivative security and hidden economic risk. (English) Zbl 1425.91408
Summary: Asset allocation with a derivative security is studied in a hidden, Markovian regime-switching, economy using filtering theory and the martingale approach. A generalized delta-hedged ratio and a generalized elasticity of an option are introduced to accommodate the presence of the information state process and the derivative security. Malliavin calculus is applied to derive a solution for a general utility function which includes an exponential utility, a power utility, and a logarithmic utility. A compact solution is obtained for a logarithmic utility. Some economic implications of the solutions are discussed.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G10 | Portfolio theory |
| 60G44 | Martingales with continuous parameter |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 91B16 | Utility theory |
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