64 research outputs found
Dual and backward SDE representation for optimal control of non-Markovian SDEs
We study optimal stochastic control problem for non-Markovian stochastic
differential equations (SDEs) where the drift, diffusion coefficients, and gain
functionals are path-dependent, and importantly we do not make any ellipticity
assumption on the SDE. We develop a controls randomization approach, and prove
that the value function can be reformulated under a family of dominated
measures on an enlarged filtered probability space. This value function is then
characterized by a backward SDE with nonpositive jumps under a single
probability measure, which can be viewed as a path-dependent version of the
Hamilton-Jacobi-Bellman equation, and an extension to expectation
Ambiguous volatility and asset pricing in continuous time
This paper formulates a model of utility for a continuous time framework that
captures the decision-maker's concern with ambiguity about both volatility and
drift. Corresponding extensions of some basic results in asset pricing theory
are presented. First, we derive arbitrage-free pricing rules based on hedging
arguments. Ambiguous volatility implies market incompleteness that rules out
perfect hedging. Consequently, hedging arguments determine prices only up to
intervals. However, sharper predictions can be obtained by assuming preference
maximization and equilibrium. Thus we apply the model of utility to a
representative agent endowment economy to study equilibrium asset returns. A
version of the C-CAPM is derived and the effects of ambiguous volatility are
described
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