The following Question is about value-at-risk.

An insurance company has sold a number of insurance policies. Each of these insurance policy covers 2 risks: Risk 1 and Risk 2. You are given that o The total number of claim events (including both risk 1 and risk 2) made in these insurance policies has Poisson distribution with mean 2000. 0 Historical data reveals that 60% of the claims are caused by risk 1 and 40% of the claims are caused by risk 2. o For risk 1, loss amount in a single claim event has exponential distribution with mean 500 and o For risk 2, loss amount in a single claim event has exponential distribution with mean 1000. 0 An ordinary deductible of $500 per loss is imposed to all claim events caused by risk 2 and no coverage modification is imposed to risk 1. Find the value-atrisk of the aggregate claim payment at 95% security level. Provide full justification to your answer. (Hint: Separate the total claim payment into two parts)