Mathematics Colloquium

Add to Calendar 04/27/2017 15:35:0004/27/2017 16:35:0015Mathematics ColloquiumWe have two mathematics clinic presentations today: Speaker #1: Thanadol Sukjitnittayakarn Advisor: Dr. Liu Title: Reduction of truncation error for a finite difference scheme for the Black Scholes equation Abstract: Finite difference methods are simplest and oldest methods among all the numerical techniques to approximate the solution of partial differential equation (PDEs). The derivatives in the partial differential equation are approximated by finite difference formulas. The error between the numerical solution and the exact solution is determined by the error between a differential operator and a difference operator. This error is called the discretization error or truncation error. The term truncation error reflects the fact that a finite part of a Taylor series is used in the approximation. In this work we will analyze the truncation error for a finite difference scheme for the Black-Scholes PDE for the valuation of an option. Numerical results are provided. Speaker #2: Chenwei Liu Advisor: Dr. Ren Title: Optimal investment, consumption and life insurance Abstract: We considered the problem of optimal investment, consumption and life insurance acquisition for a wage earner who uses an expected utility criterion with constant relative risk aversion (CRRA) preferences. The market model is complete, continuous, the uncertainty is driven by Brownian motion and the stock price has mean reverting drift. We applied the Hamilton-Jacobi-Bellman (HJB) equation associated with maximizing the expected utility criterion to solve the problem. This in turn provides the optimal investment, consumption and life insurance acquisition. We also explored the impact of stochastic market price of risk (MPR) on the optimal investment strategies.  Refreshments are available at 3:00 PM in SC 313F. The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. PLEASE NOTE THIS EVENT TAKES PLACE ON A FRIDAY.Science Center Room 323Paul Eloepeloe1@udayton.eduNo04/27/2017

Thursday, April 27

Time: 3:35 p.m. — 4:35 p.m.

Location: Science Center Room 323

Tags:  Arts and Sciences, Colloquia, Mathematics, Sciences

Cost:  Free

We have two mathematics clinic presentations today:

Speaker #1: Thanadol Sukjitnittayakarn

Advisor: Dr. Liu

Title: Reduction of truncation error for a finite difference scheme for the Black Scholes equation

Abstract: Finite difference methods are simplest and oldest methods among all the numerical techniques to approximate the solution of partial differential equation (PDEs). The derivatives in the partial differential equation are approximated by finite difference formulas. The error between the numerical solution and the exact solution is determined by the error between a differential operator and a difference operator. This error is called the discretization error or truncation error. The term truncation error reflects the fact that a finite part of a Taylor series is used in the approximation. In this work we will analyze the truncation error for a finite difference scheme for the Black-Scholes PDE for the valuation of an option. Numerical results are provided.

Speaker #2: Chenwei Liu

Advisor: Dr. Ren

Title: Optimal investment, consumption and life insurance

Abstract: We considered the problem of optimal investment, consumption and life insurance acquisition for a wage earner who uses an expected utility criterion with constant relative risk aversion (CRRA) preferences. The market model is complete, continuous, the uncertainty is driven by Brownian motion and the stock price has mean reverting drift. We applied the Hamilton-Jacobi-Bellman (HJB) equation associated with maximizing the expected utility criterion to solve the problem. This in turn provides the optimal investment, consumption and life insurance acquisition. We also explored the impact of stochastic market price of risk (MPR) on the optimal investment strategies. 

Refreshments are available at 3:00 PM in SC 313F.

The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. PLEASE NOTE THIS EVENT TAKES PLACE ON A FRIDAY.

Contact Information:

Name:  Paul Eloe
Email:  peloe1@udayton.edu