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Consider an insurance company exposed to a stochastic economic environmentthat contains two kinds of risk. The first kind is the insurance risk caused bytraditional insurance claims, and the second kind is the financial riskresulting from investments. Its wealth process is described in a standarddiscrete-time model in which, during each period, the insurance risk isquantified as a real-valued random variable $X$ equal to the total amount ofclaims less premiums, and the financial risk as a positive random variable $Y$equal to the reciprocal of the stochastic accumulation factor. This risk modelbuilds an efficient platform for investigating the interplay of the two kindsof risk. We focus on the ruin probability and the tail probability of theaggregate risk amount. Assuming that every convex combination of thedistributions of $X$ and $Y$ is of strongly regular variation, we derive someprecise asymptotic formulas for these probabilities with both finite andinfinite time horizons, all in the form of linear combinations of the tailprobabilities of $X$ and $Y$. Our treatment is unified in the sense that nodominating relationship between $X$ and $Y$ is required.

Interplay of insurance and financial risks in a discrete-time model with strongly regular variation