# Ruin Probabilities For Some Collective Risk Reserve Processes With Stochastic Investment And Inflation

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Basically, Insurance firms collect premiums and pay claims. Not to go bankrupt in a highly competitive market, insurance companies engage in several investment portfolios which can be classified as either investments with fixed or stochastic returns but not both. Companies engaging in these investments need to monitor their investments and re-asses their strategy periodically in order not to be bankrupt. This study provided a model for the risk reserve process of the insurance firm involved in both investment portfolios at the same time, as against what is obtainable in several other works and investigated the ruin model through computation of ruin probabilities. The specific objectives were to: (i) develop a collective risk model with stochastic investment and inflation, (ii) determine the ruin probabilities for the model, (iii) compare various cases of the model and investigate the effect of stochastic investment and inflation and (iv) apply the model to real life data. A collective risk model representing situations where ruin is caused by claims and/or investments respectively was formulated. The model was converted into differential equations and were resolved using the theory of confluence hypergeometric functions. R-statistical software was used with â€œfAsian Optionsâ€ package to generate results. These results were generated at varying values of capital, claim size, premium rate, claims arrival rate, investment, interest, drift and volatility. The following were the findings of the study:rn1. A collective risk model with stochastic investment and inflation was developed and resolved into ruin probabilities. rn2. The results show that ruin probabilities for either claims or investments decrease as capital increases, irrespective of the values of premium rate, average claim size, arrival rate of claims and returns from investments. rn3. Using various cases, ruin probabilities decrease when average claim size, claim arrival rate, volatility and fraction of investments are increased. rn4. Ruin probability attributable to claims was found to be constant when claim arrival rate is set to zero while other parameters are kept constant. rn5. Ruin probabilities for the model is independent of inflation and decrease as fraction of investments into risky asset decreases. The lowest value was obtained when there is no investment with stochastic returns while the highest value was obtained when all investments are assumed to be with stochastic returns. rn6. The results from real life data, were comparable to the findings from empirical data. rnIt can be concluded from this study that investing in markets with stochastic returns is comparatively more risky than either investing part or all resources into fixed returned market. In particular, the lowest ruin probability from investment were obtained when all resources were plunged into markets with fixed returns. It is therefore recommended to invest in markets with both fixed and stochastic returns. This study also showed that ruin probabilities were independent of inflation.

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