[ugrads] Math Finance, Stochastic Analysis and Machine Learning Seminar: First seminar on 8.28

Matthew Dixon mdixon7 at stuart.iit.edu
Fri Aug 24 15:55:39 CDT 2018


Dear All,

Please join us for our first Math Finance seminar of the Fall, given by our
own Sergey Nadtochiy. Please see below for the talk abstract.

The Math Finance seminars shall be held every Tuesday (and typically
Thursdays also) at the same time (room number subject to change).  Many of
the talk abstracts already appear on the website (here
<https://science.iit.edu/applied-mathematics/mathematical-finance-and-stochastic-analysis-seminar>).
We may have the occasion talk from external speakers on different days of
the week also.


*Title: Optimal Contract for a Fund Manager, with Capital Injections and
Endogenous Trading ConstraintsSpeaker: Sergey Nadtochiy*

*Date & Location: Tuesday, August 28th, 11:25-12:40pm, in RE 121*

*arXiv: https://arxiv.org/abs/1802.09165 <https://arxiv.org/abs/1802.09165>*

*Abstract*. In this paper, we construct a solution to the optimal contract
problem for delegated
portfolio management of the fist-best (risk-sharing) type. The novelty of
our result is (i)
in the robustness of the optimal contract with respect to perturbations of
the wealth process
(interpreted as capital injections), and (ii) in the more general form of
principal’s objective
function, which is allowed to depend directly on the agent’s strategy, as
opposed to being a
function of the generated wealth only. In particular, the latter feature
allows us to incorporate
endogenous trading constraints in the contract. We reduce the optimal
contract problem to
the following inverse problem: for a given portfolio (defined in a feedback
form, as a random
field), construct a stochastic utility whose optimal portfolio coincides
with the given one. We
characterize the solution to this problem through a Stochastic Partial
Differential Equation
(SPDE), prove its well-posedness, and compute the solution explicitly in
the Black-Scholes
model.

Matthew Dixon, Ph.D., FRM
Assistant Professor
Department of Applied Math
Pritzker 106E
Illinois Institute of Technology
Chicago IL 60616
Homepage <http://mypages.iit.edu/~mdixon7/>
LinkedIn <https://www.linkedin.com/in/mfrdixon>
ResearchGate <https://www.researchgate.net/profile/Matthew_Dixon>
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