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Optimal Multi-Period Asset Allocation for Life Insurance Policies

Optimal Multi-Period Asset Allocation for Life Insurance Policies. Hong-Chih Huang Associate Professor, Department of Risk Management and Insurance, National Chengchi University, Taiwan Yung-Tsung Lee

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Optimal Multi-Period Asset Allocation for Life Insurance Policies

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  1. Optimal Multi-Period Asset Allocation for Life Insurance Policies Hong-Chih Huang Associate Professor, Department of Risk Management and Insurance, National Chengchi University, Taiwan Yung-Tsung Lee Ph.D. Student, Department of Risk Management and Insurance, National Chengchi University, Taiwan

  2. Purpose • employ a multi-assets model and investigate the multi-period optimal asset allocation on life insurance reserves. for a general portfolio of life insurance policy

  3. Literature Review • Marceau and Gaillardetz (1999) • Huang and Cairns (2006).

  4. Contributions • provide a good contribution on solving multi-period asset allocation problems of the application of life insurance policies. • find that the optimal investment strategy will be very different under different durations of policy portfolios.

  5. The liability model

  6. The liability model

  7. Multi-asset return model

  8. 2-2. Multi-asset model

  9. Moments of Loss Functions

  10. Three Cases of Policy Portfolios • All cases have 10 endowments policies, with the same term 10 years and the same sum assumed 1. • Case A: 10 new policies at the valuation date Case B: 10 policies with different uniform maturity dates Case C: The maturity date is selected randomly.

  11. Three Cases of Policy Portfolios • The maturity dates of case C are as follows:

  12. Optimal asset allocation • Single-Period Rebalance • Multi-Period Rebalance

  13. Single-Period RebalanceMean–variance plot: case B

  14. Mean–variance plot: case B • An efficient frontier can be found at the left part of the plot. • Insurance company can minimize variance of loss under a contour line of mean; or minimize mean under a contour line of variance.

  15. Objective Function

  16. Optimal Asset AllocationSingle-period rebalance

  17. Optimal Asset AllocationMulti-period rebalance case A and case B

  18. Optimal Asset AllocationMulti-period rebalance case A and case B(with short constraints)

  19. 4-2. Multi-period rebalance - case A and case B • The holding pattern of riskless/risky asset are totally different between case A and case B, regardless of a short constrain exist or not. • Under case A, the proportion of cash is increasing and the proportion of risky assets is decreasing; whereas an opposite pattern arise under case B.

  20. Optimal Asset AllocationMulti-period rebalance-case C

  21. Multi-period rebalance- case C • Due to the randomness of the maturity dates of the policies, the optimal investment strategy appears a saw-toothed variation, whereas the pattern is similar with case B (the uniform case). • The optimal asset allocation with short constrain under case C is almost the same as the without constrain one, so we display the result of without constrain only.

  22. Sensitivity Analysis of k The optimal asset allocations of multi-period rebalance, k=0.5, 1 and2

  23. Sensitivity Analysis of asset model High excess mean: The optimal asset allocations under case B

  24. Sensitivity Analysis of asset model High variance: The optimal asset allocations under case B

  25. The Case of large sample • We examine the optimal asset allocations under 4 policy portfolios. • These 4 portfolios have a same statistic property: the maturity dates of a same portfolio has p-value 0.9513 under chi-square goodness of fit test. • The null hypothesis is that the maturity dates are selected form a discrete uniform distribution. • Thus, these 4 portfolios are unlike uniformly distributed in a statistical sense.

  26. The Case of large sample The optimal asset allocation of the 4 special portfolios

  27. The Case of large sample The optimal asset allocation of a specific portfolio

  28. 6. Conclusion • This paper successfully derives the formulae of the first and second moments of loss functions based on a multi-assets return model. • With these formulae, we can analyze the portfolio problems and obtain optimal investment strategies. • Under single-period rule, we found an efficient frontier in the mean-variance plot. This efficient frontier can be found under an arbitrary policies portfolio.

  29. 6. Conclusion • In multi-period case, we found that the optimal asset allocation can vary enormously under different policy portfolios. • A. “Top-Down” strategy for a single policy • B. “Down-Top” strategy for a portfolio with numbers of policies

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