Stochastic modelling (insurance)

This page is concerned with the stochastic modelling as applied to the insurance industry. For other stochastic modelling applications, please see Monte Carlo method and Stochastic asset models. For mathematical definition, please see Stochastic process. "Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s). Its application initially started in physics. It is now being applied in engineering, life sciences, social sciences, and finance. See also Economic capital. Like any other company, an insurer has to show that its assets exceeds its liabilities to be solvent. In the insurance industry, however, assets and liabilities are not known entities. They depend on how many policies result in claims, inflation from now until the claim, investment returns during that period, and so on. So the valuation of an insurer involves a set of projections, looking at what is expected to happen, and thus coming up with the best estimate for assets and liabilities, and therefore for the company's level of solvency. The simplest way of doing this, and indeed the primary method used, is to look at best estimates. The projections in financial analysis usually use the most likely rate of claim, the most likely investment return, the most likely rate of inflation, and so on. The projections in engineering analysis usually use both the most likely rate and the most critical rate. The result provides a point estimate - the best single estimate of what the company's current solvency position is, or multiple points of estimate - depends on the problem definition.