3,349 research outputs found
Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact
We study an optimal execution problem with uncertain market impact to derive
a more realistic market model. We construct a discrete-time model as a value
function for optimal execution. Market impact is formulated as the product of a
deterministic part increasing with execution volume and a positive stochastic
noise part. Then, we derive a continuous-time model as a limit of a
discrete-time value function. We find that the continuous-time value function
is characterized by a stochastic control problem with a Levy process.Comment: 17 pages. Forthcoming in "Communications on Stochastic Analysis.
"A Semi-group Expansion for Pricing Barrier Options"
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, we propose a concrete approximation formula under a stochastic volatility model and demonstrate its validity by some numerical experiments.
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