Quadratic hedging strategies in incomplete financial markets

Thời gian: 14:00 đến 16:00 Ngày 11/06/2021

Địa điểm: Online qua Zoom

Báo cáo viên: TS. Nguyễn Trần Thuận - Vinh University, Vietnam and Saarland University, Germany

Tóm tắt:

In this talk, we discuss about the quadratic hedging in incomplete financial markets which is a typical problem arisen from financial mathematics.

Suppose that a risky asset is modelled by a stochastic process S possibly possessing jumps. We consider two standard settings where S is a (local) martingale or a semimartingale under a reference measure.

In the martingale framework, the quadratic hedging problem can be "solved" by the Kunita-Watanabe decomposition, which is a kind of orthogonal decomposition in the space L_2, and this yields the so-called mean variance hedging strategies. In the semimartingale setting, one exploits another orthogonal decomposition so-called Follmer-Schweizer decomposition and it gives the local risk minimizing strategies.

Those quadratic hedging strategies are usually provided in general forms which leads to some disadvantage for numerical methods. We also discuss some situations with typical methods where one can derive explicitly formulas for those strategies which enable some numerical computation. In particular, we focus on the exponential Levy models as an illustrative example.

Meeting ID: 214 980 4183
Passcode: 123456