Static use of options in dynamic portfolio optimization under transaction costs and solvency constraints

Stefano Baccarin ()
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Stefano Baccarin: Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino, Italy

No 63, Working papers from Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino

Abstract: We study a dynamic portfolio optimization problem where it is possible to invest in a risk-free bond, in a risky stock modeled by a lognormal diffusion and in call options written on the stock. The use of the options is limited to static strategies at the beginning of the investment period. The investor faces transaction costs with a fixed component and solvency constraints and the objective is to maximize the expected utility of the final wealth. We characterize the value function as a constrained viscosity solution of the associated quasi-variational inequality and we prove the local uniform convergence of a Markov chain approximation scheme to compute numerically the optimal solution. Because of transaction costs and solvency constraints the options cannot be pefectly replicated and despite the restriction to static policies our numerical results show that in most cases the investor will keep a significant part of his portfolio invested in options.

Keywords: Dynamic Portfolio Management; Incomplete Markets; Static Use of Options; Impulse Control; Viscosity Solutions; Markov Chain Approximations. (search for similar items in EconPapers)
JEL-codes: C61 C63 G11 G13 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2019-05
New Economics Papers: this item is included in nep-bec, nep-ore and nep-upt
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