186,637 research outputs found
Exact Simulation for Diffusion Bridges: An Adaptive Approach
Exact simulation approaches for a class of diffusion bridges have recently been proposed based on rejection sampling techniques. The existing rejection sampling methods may not be practical owing to small acceptance probabilities. In this paper we propose an adaptive approach that improves the existing methods significantly under certain scenarios. The idea of the new method is based on a layered process, which can be simulated from a layered Brownian motion with reweighted layer probabilities. We will show that the new exact simulation method is more efficient than existing methods theoretically and via simulation
A New Class of Backward Stochastic Partial Differential Equations with Jumps and Applications
We formulate a new class of stochastic partial differential equations
(SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which
allow the high-order integral-partial differential operators into both drift
and diffusion coefficients. Under certain type of Lipschitz and linear growth
conditions, we develop a method to prove the existence and uniqueness of
adapted solution to these B-SPDEs with jumps. Comparing with the existing
discussions on conventional backward stochastic (ordinary) differential
equations (BSDEs), we need to handle the differentiability of adapted triplet
solution to the B-SPDEs with jumps, which is a subtle part in justifying our
main results due to the inconsistency of differential orders on two sides of
the B-SPDEs and the partial differential operator appeared in the diffusion
coefficient. In addition, we also address the issue about the B-SPDEs under
certain Markovian random environment and employ a B-SPDE with strongly
nonlinear partial differential operator in the drift coefficient to illustrate
the usage of our main results in finance.Comment: 22 pagea, 1 figur
- …