Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this talk, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index $H \in (0, 1)$). We rigorously establish a first order approximation of the optimal value, when the return and volatility of the underlying asset are functions of a stationary slowly varying fractional Ornstein-Uhlenbeck process. We prove that this approximation can be also generated by the zeroth order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this strategy in a specific family of admissible strategies. If time permits, we will also discuss the problem under fast mean-reverting fractional stochastic environment.

Joint work with Ruimeng Hu (UCSB).

Bio:

Jean-Pierre Fouque

Ph.D. in Mathematics, University Pierre et Marie Curie, Paris 6, 1979.

Jean-Pierre Fouque held positions at the CNRS and at the Ecole Polytechique in France, before joining North Carolina State University in 1998 where he started the Masters of Financial Mathematics.

In 2006, he joined the department of Statistics and Applied Probability at the University of California Santa Barbara where he is a Distinguished Professor and Co-director of the Center for Financial Mathematics and Actuarial Research (CFMAR).

His research is in the domain of random media with applications ranging from wave propagation phenomena to financial mathematics. He published over one hundred research articles and co-authored three books:

"Derivatives in Financial Markets with Stochastic Volatility" (Cambridge University Press, 2000),

"Wave Propagation and Time Reversal in Randomly Layered Media" (Springer, 2007), and

"Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives" (Cambridge University Press, 2011).

He co-edited the "Handbook on Systemic Risk" (CUP, 2013), and he was a member of the Advisory Committee of the U.S. Office of Financial Research (2012-2015).

He is currently Editor-in-Chief of the SIAM Journal on Financial Mathematics and President of the Bachelier Finance Society.

Jean-Pierre Fouque is a Fellow of the Institute of Mathematical Statistics since 2009 and a SIAM Fellow since 2011.

His web page: www.pstat.ucsb.edu/faculty/fouque