Partial hedging and cash requirements in discrete time. (English) Zbl 1468.91159
Summary: This paper develops a discrete time version of the continuous time model of B. Bouchard et al. [SIAM J. Control Optim. 48, No. 5, 3123–3150 (2010; Zbl 1202.49028)], for the problem of finding the minimal initial data for a controlled process to guarantee reaching a controlled target with probability one. An efficient numerical algorithm, based on dynamic programming, is proposed for the quantile hedging of standard call and put options, exotic options and quantile hedging with portfolio constraints. The method is then extended to solve utility indifference pricing, good-deal bounds and expected shortfall problems.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 93E20 | Optimal stochastic control |
| 90C39 | Dynamic programming |
Keywords:
quantile hedging; stochastic optimal control; dynamic programming; utility indifference pricing; expected shortfallCitations:
Zbl 1202.49028References:
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