18,440 research outputs found
Infinite horizon optimal control of forward-backward stochastic differential equations with delay
We consider a problem of optimal control of an infinite horizon system
governed by forward-backward stochastic differential equations with delay.
Sufficient and necessary maximum principles for optimal control under partial
information in infinite horizon are derived. We illustrate our results by an
application to a problem of optimal consumption with respect to recursive
utility from a cash flow with delay
Singular recursive utility
We introduce the concept of singular recursive utility. This leads to a kind
of singular BSDE which, to the best of our knowledge, has not been studied
before. We show conditions for existence and uniqueness of a solution for this
kind of singular BSDE. Furthermore, we analyze the problem of maximizing the
singular recursive utility. We derive sufficient and necessary maximum
principles for this problem, and connect it to the Skorohod reflection problem.
Finally, we apply our results to a specific cash flow. In this case, we find
that the optimal consumption rate is given by the solution to the corresponding
Skorohod reflection problem
A BSDE-based approach for the optimal reinsurance problem under partial information
We investigate the optimal reinsurance problem under the criterion of
maximizing the expected utility of terminal wealth when the insurance company
has restricted information on the loss process. We propose a risk model with
claim arrival intensity and claim sizes distribution affected by an
unobservable environmental stochastic factor. By filtering techniques (with
marked point process observations), we reduce the original problem to an
equivalent stochastic control problem under full information. Since the
classical Hamilton-Jacobi-Bellman approach does not apply, due to the infinite
dimensionality of the filter, we choose an alternative approach based on
Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize
the value process and the optimal reinsurance strategy in terms of the unique
solution to a BSDE driven by a marked point process.Comment: 30 pages, 3 figure
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