## JMI2009A-1 The random walk model revisited (pp.1-6)

Author(s)： Takehiro Hirotsu and Setsuo Taniguchi

J. Math-for-Ind. **1A** (2009) 1-6.

- File： JMI2009A-1.pdf (119KB)

Abstract

The random walk model was introduced and investigated by D. Heyer [1]. It is a loss development model, where the geometric Brownian motion, which is frequently used in Mathematical Finance (for example, recall the famous Black-Scholes option pricing formula), is applied to cumulative losses. While Heyer applied his model to estimating INBR (incurred but not yet reported) losses of each accident year, he made no observation on the year-on-year loss (the loss to be paid in the specific future year). To estimate year-on-year losses is one of urgent issues in the non-life insurance industry. In this paper, as another application of the random walk model, the conditional distribution and the conditional confidence interval of the year-on-year loss to be paid in the specific future year, being given the cumulative losses of the present, will be investigated.

Keyword(s). random walk model, IBNR, geometric Brownian motion, distribution, confidence interval, cumulative loss