A remark on smooth solutions to a stochastic control problem with a\n power terminal cost function and stochastic volatilities

2014/05/14 by Yalçin Aktar, Erik Taflin, Aktar, Yalçin +1
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #35K55 #49J55 #60H30 #93E20 #Advanced Queuing Theory Analysis #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1405.3566

openalex publication_date 2014/05/14 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Incomplete financial markets are considered, defined by a multi-dimensional\nnon-homogeneous diffusion process, being the direct sum of an It ^o process\n(the price process), and another non-homogeneous diffusion process (the\nexogenous process, representing exogenous stochastic sources). The drift and\nthe diffusion matrix of the price process are functions of the time, the price\nprocess itself and the exogenous process.\n In the context of such markets and for power utility functions, it is proved\nthat the stochastic control problem consisting of optimizing the expected\nutility of the terminal wealth, has a classical solution (i.e. C^1,2).\n This result paves the way to a study of the optimal portfolio problem in\nincomplete forward variance stochastic volatility models, along the lines of\nRef: Ekeland et al.\n

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