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
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
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
