Paper: arXiv 2410.20060

Abstract

This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, of which the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint are special cases. Following Cuoco (1997), we build the artificial markets to derive the dual problem and prove the existence of the original problem. With additional discussions, we extend his uniformly bounded assumption on the interest rate to an almost surely finite expectation condition and enlarge his uniformly bounded assumption on the income process to a bounded expectation condition. Moreover, we propose a dual control neural network approach to compute tight lower and upper bounds for the original problem, which can be utilized in more general cases than the simulation of artificial markets strategies (SAMS) approach in Bick et al. (2013). Finally, we conclude that when considering the trading constraints, the individual will reduce his or her demand for life insurance.

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper uses advanced mathematical techniques like dual control, artificial markets, and rigorous proofs of existence under weak assumptions, but the empirical validation is purely theoretical simulation (neural network on synthetic data) without real backtests or live data.

Research Flowchart

  flowchart TD
  A["Research Goal: Constrained Portfolio Optimization in a Life-Cycle Model"] --> B["Methodology: Dual Control via Artificial Markets"]
  B --> C["Input: Stochastic Income & Asset Processes"]
  C --> D{"Computation: Dual Control Neural Network"}
  D -->|Training| E["Tight Lower & Upper Bounds"]
  E --> F["Key Findings: Trading Constraints Reduce Life Insurance Demand"]

Cited References (158)

  1. Life annuitization: Why and how much? (2006)
  2. Life insurance and pension contracts I : The time additive life cycle model (2015)
  3. Life insurance and pension contracts II : The life cycle model with recursive utility (2016)
  4. Life-cycle planning with CEV model and time-inconsistent preferences (2024)
  5. Hedging recessions (2019)
  6. Optimal portfolio policies with borrowing and shortsale constraints (2000)
  7. Constrained monotone mean-variance problem with random coefficients — → 2212.14188
  8. Constrained utility deviation-risk optimization and time-consistent HJB equation (2020)
and 150 more
  1. Utility maximization under trading constraints with discontinuous utility (2019)
  2. Constrained stochastic LQ control with random coefficients, and application to portfolio selection (2005)
  3. A life cycle model of life insurance purchases (1973)
  4. Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution (2012)
  5. Optimal life insurance and annuity decisions under money illusion (2025)
  6. \text The Logic of Finance (2009)
  7. Demand for non-life insurance under habit formation (2021)
  8. Asset Prices under Habit Formation and Catching Up with the Joneses (1990)
  9. Optimal Consumption-Portfolio Policies With Habit Formation1 (1992)
  10. Aspects of the Theory of Risk-bearing (1965) — link
  11. Risk Aversion in the Small and in the Large (1964)
  12. The design of an optimal insurance policy (1979)
  13. Aspects of rational insurance purchasing (1968)
  14. Insurance and consumption: The continuous time case (1986)
  15. Uncertainty and the Welfare Economics of Medical Care (1963)
  16. Optimal insurance demand under marked point processes shocks (2000)
  17. Optimal investment, consumption–leisure, insurance and retirement choice (2013)
  18. Optimal consumption, investment and insurance with insurable risk for an investor in a L 'e vy market (2010)
  19. Explicit solutions of optimal consumption, investment and insurance problems with regime switching (2014)
  20. Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle (2020)
  21. Dynamic derivative strategies (2003)
  22. The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts (2012)
  23. Derivatives trading for insurers (2019)
  24. Habit formation and the demand for insurance (1996)
  25. Habit formation: A resolution of the equity premium puzzle (1990)
  26. Consumption habits and humps (2017)
  27. A World at Risk: Closing the Insurance Gap (2018)
  28. Optimal insurance in a continuous-time model (2006)
  29. Personal Non-Life Insurance Decisions And The Welfare Loss From Flat Deductibles (2019)
  30. Intertemporally dependent preferences and the volatility of consumption and wealth (1989)
  31. Life-cycle portfolio choice with additive habit formation preferences and uninsurable labor income risk (2006)
  32. Optimum consumption and portfolio rules in a continuous-time model (1971)
  33. Optimal consumption and asset allocation with unknown income growth (2009)
  34. Generalizing the permanent-income hypothesis: Revisiting Friedman ’s conjecture on consumption (2006)
  35. Earnings uncertainty and aggregate wealth accumulation (1991)
  36. Consumption and habit formation when time horizon is finite (2009)
  37. The interaction between time-nonseparable preferences and time aggregation (1993)
  38. Asset prices in an exchange economy with habit formation (1991)
  39. Life-cycle portfolio choice with additive habit formation preferences and uninsurable labor income risk (2007)
  40. Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences (2008)
  41. Loss aversion, habit formation and the term structures of equity and interest rates (2015)
  42. Portfolio choice with internal habit formation: A life-cycle model with uninsurable labor income risk (2003)
  43. Optimal insurance arrangements (1975)
  44. Applied Stochastic Control of Jump Diffusions (2007)
  45. Ordinary Differential Equations with Applications (2006)
  46. Pro-cyclical mortality across socioeconomic groups and health status (2015)
  47. The best of times, the worst of times: understanding pro-cyclical mortality (2015)
  48. Effect of the Great Recession on regional mortality trends in Europe (2019)
  49. Business cycle and mortality in Spain (2021)
  50. Are recessions good for your health? (2000)
  51. Unemployment and mortality: Evidence from the PSID (2014)
  52. Recessions and seniors’ health, health behaviors, and healthcare use: Analysis of the Medicare Current Beneficiary Survey (2012)
  53. The time-varying relationship between mortality and business cycles in the USA (2017)
  54. Good times make you sick (2003)
  55. Mortality and macroeconomic conditions: what can we learn from France? (2019)
  56. Recessions, healthy no more? (2015)
  57. Stochastic mortality dynamics driven by mixed fractional Brownian motion (2022)
  58. Longevity bond pricing under stochastic interest rate and mortality with regime-switching (2013)
  59. Optimal retirement consumption with a stochastic force of mortality (2012)
  60. Valuation of equity-indexed annuity under stochastic mortality and interest rate (2010)
  61. Matrix Riccati Equations in Control and Systems Theory (2012)
  62. Kalman filtering of generalized Vasicek term structure models (1999)
  63. Optimal pension management in a stochastic framework (2004)
  64. Stochastic Control of Partially Observable Systems (2004)
  65. Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause (2018)
  66. Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility (Actuarial Research Paper No. 186) (2008)
  67. Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund (2001)
  68. The shift from defined benefit to defined contribution pension plans–implications for asset allocation and risk management (2006)
  69. Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans (2006)
  70. Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk (2017)
  71. Consumption and portfolio choice over the life cycle (2005)
  72. Optimal investment strategies in the presence of a minimum guarantee (2003)
  73. Optimal design of the guarantee for defined contribution funds (2004)
  74. Actuarial Mathematics for Life Contingent Risks (2013)
  75. Pension funds with a minimum guarantee: a stochastic control approach (2011)
  76. Optimal investment of DC pension plan under short-selling constraints and portfolio insurance (2019)
  77. Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan (2020)
  78. A yield-factor model of interest rates (1996)
  79. \text Monetary Policy Report to the Congress - February,2001 (2001)
  80. \text Monetary Policy Report to the Congress - July,2008 (2008)
  81. \text Monetary Policy Report to the Congress - June,2020 (2020)
  82. Applications of mathematics (1975)
  83. On graduation by mathematical formula (1988)
  84. Optimal investment choices post-retirement in a defined contribution pension scheme (2004)
  85. The US Treasury yield curve: 1961 to the present (2007)
  86. Forecasting, Structural Time Series Models and the Kalman Filter (1990)
  87. Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework (2013)
  88. On the verification theorem of dynamic portfolio-consumption problems with stochastic market price of risk (2011)
  89. \text Publication 575 - Pension and Annuity Income (2019)
  90. Optimal annuity risk management (2011)
  91. On the Stability of Continuous-Time Portfolio Problems with Stochastic Opportunity Set (2004)
  92. Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model (2017)
  93. Optimal dynamic asset allocation of pension fund in mortality and salary risks framework (2015)
  94. Stochastic optimal control of DC pension funds (2008)
  95. Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework (2014)
  96. Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints (2016)
  97. Optimal asset allocation for DC pension plans under inflation (2012)
  98. Optimal savings management for individuals with defined contribution pension plans (2015)
  99. Optimal portfolios with stochastic interest rates and defaultable assets (2004)
  100. On the law of mortality and the construction of annuity tables (1860)
  101. Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework (2017)
  102. Dynamic asset allocation with stochastic income and interest rates (2010)
  103. \text Pension Markets in Focus 2020 (2020)
  104. \text Pensions part 2 - Defined Contribution Plans (2020)
  105. Graphical discussion of the roots of a quartic equation (1922)
  106. Variable Annuities: What You Should Know (2009)
  107. Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model (2016)
  108. A Guide to Purolator Inc. Retirement Program Defined Contribution Pension Plan (DCPP) (2017)
  109. Constant proportion portfolio insurance in defined contribution pension plan management (2018)
  110. Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility (2018)
  111. Robust portfolio choice for a DC pension plan with inflation risk and mean-reverting risk premium under ambiguity (2021)
  112. Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk (2015)
  113. The constant elasticity of variance (CEV) model and the Legendre transform–dual solution for annuity contracts (2007)
  114. Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model (2013)
  115. Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework (2014)
  116. Stochastic Controls: Hamiltonian Systems and HJB Equations (1999)
  117. Optimal investment for a pension fund under inflation risk (2010)
  118. Consumption and investment under constraints (1994)
  119. A general equilibrium model of portfolio insurance (1995)
  120. Solving constrained consumption–investment problems by simulation of artificial market strategies (2013)
  121. Annuity and insurance choice under habit formation (2022)
  122. Dynamic equilibrium with two stocks, heterogeneous investors, and portfolio constraints (2013)
  123. Lectures from Markov Processes to Brownian Motion (2013)
  124. Optimal consumption and portfolio policies when asset prices follow a diffusion process (1989)
  125. A variational problem arising in financial economics (1991)
  126. Optimal consumption and equilibrium prices with portfolio constraints and stochastic income (1997)
  127. Martingale and duality methods for utility maximization in an incomplete market (1991)
  128. Convex duality in constrained portfolio optimization (1992)
  129. Hedging contingent claims with constrained portfolios (1993)
  130. Probabilities and Potential, C: Potential Theory for Discrete and Continuous Semigroups (2011)
  131. A Monte Carlo method for optimal portfolios (2003)
  132. Martingales and arbitrage in multiperiod securities markets (1979)
  133. Evaluating portfolio policies: A duality approach (2006)
  134. Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case (1991)
  135. Solving life-cycle problems with biometric risk by artificial insurance markets (2022)
  136. Labor income, borrowing constraints, and equilibrium asset prices (1993)
  137. Viable prices in financial markets with solvency constraints (1995)
  138. Asset pricing with linear collateral constraints (1995)
  139. Portfolio choice and life insurance: The CRRA case (2008)
  140. Optimal portfolio and consumption decisions for a “small investor” on a finite horizon (1987)
  141. Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints (2013)
  142. Near-optimal asset allocation in financial markets with trading constraints (2022)
  143. Limit Theorems for Stochastic Processes (2013)
  144. On utility maximization under convex portfolio constraints (2013)
  145. Extremal problems with convex functionals that are lower semicontinuous with respect to convergence in measure (1976)
  146. Optimal investment and consumption with labor income in incomplete markets (2020)
  147. Convex Analysis Princeton University Press (1970)
  148. A duality method for optimal consumption and investment under short-selling prohibition. I . G eneral market coefficients (1992)
  149. Optimal life insurance with no-borrowing constraints: duality approach and example (2016)
  150. Neural networks fail to learn periodic functions and how to fix it (2020)

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