9 research outputs found
Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equations
We consider the problem of optimal portfolio selection under forward
investment performance criteria in an incomplete market. The dynamics of the
prices of the traded assets depend on a pair of stochastic factors, namely, a
slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic
volatility). We analyze the associated forward performance SPDE and provide
explicit formulae for the leading order and first order correction terms for
the forward investment process and the optimal feedback portfolios. They both
depend on the investor's initial preferences and the dynamically changing
investment opportunities. The leading order terms resemble their time-monotone
counterparts, but with the appropriate stochastic time changes resulting from
averaging phenomena. The first-order terms compile the reaction of the investor
to both the changes in the market input and his recent performance. Our
analysis is based on an expansion of the underlying ill-posed HJB equation, and
it is justified by means of an appropriate remainder estimate.Comment: 26 page
Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE
In an incomplete market, with incompleteness stemming from stochastic factors
imperfectly correlated with the underlying stocks, we derive representations of
homothetic (power, exponential and logarithmic) forward performance processes
in factor-form using ergodic BSDE. We also develop a connection between the
forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive
optimization. In addition, we develop a connection, for large time horizons,
with a family of classical homothetic value function processes with random
endowments.Comment: 34 page
A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models
This paper studies an optimal forward investment problem in an incomplete
market with model uncertainty, in which the dynamics of the underlying stocks
depends on the correlated stochastic factors. The uncertainty stems from the
probability measure chosen by an investor to evaluate the performance. We
obtain directly the representation of the power robust forward performance
process in factor-form by combining the zero-sum stochastic differential game
and ergodic BSDE approach. We also establish the connections with the
risk-sensitive zero-sum stochastic differential games over an infinite horizon
with ergodic payoff criteria, as well as with the classical power robust
expected utility for long time horizons.Comment: 27 page
Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE
In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential, and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive optimization. In addition, we develop a connection, for large time horizons, with a family of classical homothetic value function processes with random endowments