## Proceedings of Undergraduate Mathematics Day

Article

1-1-2018

#### Publication Source

Proceedings of the 2017 Undergraduate Mathematics Day

36-43

#### Abstract

The purpose of our project was to display how our personal risk preferences affect our investment decisions, if we invested on two assets: one risky asset (stock) and one risk-free asset (bank account). We considered the problem in both discrete and continuous case. In particular, the stock price follows a multinomial tree in the discrete case; and follows a Geometric Brownian motion in the continuous case. We then found the expected value of the stocks at varying times. By setting what we expect our bank account to be at those times equal to these expected values, we solved for the interest rates, at which investing on either asset are equivalent. We then incorporated risk aversion in the power utility function. Using different levels of risk aversion, we again solve for the interest rate, at which investing on either asset are equivalent. By comparing the first interest rate with the interest rate that incorporated the risk aversion, we saw how this risk aversion affects our investment decisions.

#### Keywords

risky asset, risk-free asset, binomial tree, Geometric Brownian Motion, risk aversion

#### Disciplines

Mathematics

This paper was presented Saturday, Nov. 11, 2017, as part of Undergraduate Mathematics Day at the University of Dayton. Launched in 2003, Undergraduate Mathematics Day is held in odd-numbered years and alternates with the Biennial Alumni Career Seminar. The conference coincides with the annual Schraut Memorial Lecture, named Kenneth “Doc” Schraut, a mathematics faculty member from 1940 to 1978 and department chair from 1954 to 1970.

The 2017 invited lecturer was Joseph Gallian, the Morse Alumni Distinguished University Professor of Teaching at the University of Minnesota Duluth and a past president of the Mathematical Association of America. He presented the lecture “Breaking Driver’s License Codes.”

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