Reinsurance Portfolio Optimization Horse Chasing Algorithm
- 1. Reinsurance portfolio optimization Horse chasing algorithm Xuyan (Frank) Wang, PhD M.M Validus Research www.validusre.bm July 2008
- 2. Reinsurance portfolio optimization Horse chasing algorithm Outline • Problem setting • Our approach • Horse chasing algorithm • Search strategy • Concluding remarks 2
- 3. Reinsurance portfolio optimization Horse chasing algorithm Problem setting • Input data – simulated yearly (sequence of) losses for cat events for contract • Objective: maximize expected profit E ( P ) = ∑ wi E ( Pi ) i E( ) = measure of expected value P, Pi = expected profits of the portfolio and the ith contract wi = participation or position (i.e. amount of risk taken) of the ith contract • Constraints: • Key risk measures do not exceed specific thresholds ρ k ( P) = ρ k (∑ wi Pi ) ≤ ck i ρk = risk function, ck = threshold for the kth constraint • Realistic ranges of wi 3
- 4. AEP
- 5. TVaR
- 6. OEP
- 7. Reinsurance portfolio optimization Horse chasing algorithm Two observations about horse chasing algorithm and simplified goal • Two observations about horse chasing • Difference of chasing forward and backward • Permissible range of cross numbers before speed change • Simplified goal • Continuously improve objective function • Search strategy • Do the substitution that makes the most improvement
- 8. Reinsurance portfolio optimization Portfolio construction example
- 9. Reinsurance portfolio optimization Portfolio construction example
- 12. Reinsurance portfolio optimization Horse chasing algorithm Concluding remarks • Robust • Our simpler goal is insensitive or tolerant to horse chasing algorithm logical flaws or errors • Whether it is also insensitive to input simulation data variations remained to be studied • Jointly linear assumption • Caused minor fluctuation in portfolio risk measure • Can try more jointly linear assumption • Limitations • Is beat by good human judgment and intuition