## UW-PIMS Mathematics Colloquium: Shige Peng

- Date: 05/19/2014
- Time: 14:30

Lecturer(s):
Shige Peng,

*Shandong University*
Location:

University of Washington

Topic:

Brownian motion under Knightian uncertainty and path-dependent risk

Description:

A typical measure of risk in finance must take into account of the uncertainty of probability model itself (called Knightian uncertainty). Nonlinear expectation and the corresponding non-linear distributions provides a deep and powerful tool: cumulated nonlinear i.i.d random variables of order 1/n tend to a maximal distribution, according a new law of large number, whereas, the accumulation of order 1/√n tends to a nonlinear normal distribution which is the corresponding central limit theorem. The continuous time uncertainty cumulation forms a nonlinear Brownian motion.

The related stochastic calculus under Knightian uncertainty provides us a powerful tool of valuation for path-dependent derivatives. The corresponding Feynman-Kac formula gives one to one correspondence between fully nonlinear parabolic partial differential equations and backward stochastic differential equations driven by the nonlinear Brownian motion.

The related stochastic calculus under Knightian uncertainty provides us a powerful tool of valuation for path-dependent derivatives. The corresponding Feynman-Kac formula gives one to one correspondence between fully nonlinear parabolic partial differential equations and backward stochastic differential equations driven by the nonlinear Brownian motion.

Other Information:

Location: Loew Hall 106