Paper: arXiv 2311.01692

Abstract

In this paper we model benchmark beating with the increasing convex order (ICX order). The mean constraint in the mean-variance theory of portfolio selection can be regarded as beating a constant. We then investigate the problem of minimizing the variance of a portfolio with ICX order constraints, based on which we also study the problem of beating-performance-variance efficient portfolios. The optimal and efficient portfolios are all worked out in closed form for complete markets.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper develops advanced stochastic order theory (ICX order) with extensive proofs and quantile formulations, but provides no empirical data, backtesting, or implementation details, focusing purely on theoretical optimization in complete markets.

Research Flowchart

  flowchart TD
  A["Research Goal: Model Benchmark Beating<br>using Increasing Convex Order ICX"] --> B["Methodology: ICX Order Constraints<br>Mean Constraint = Beating a Constant"]
  B --> C["Data: Complete Markets<br>Full Covariance & Return Data"]
  C --> D["Computational Process: Minimize Portfolio Variance<br>Subject to ICX Constraints"]
  D --> E["Outcome 1: Closed-Form Optimal Portfolios"]
  D --> F["Outcome 2: Beating-Performance-Variance<br>Efficient Portfolios"]
  E --> G["Final Result: Complete analytical solutions<br>for equities/general portfolio management"]
  F --> G

Cited References (139)

  1. Different Approaches to Risk Estimation in Portfolio Theory (2004)
  2. Practical Risk‐Adjusted Performance Measurement (2013)
  3. Arrow–Debreu equilibria for rank-dependent utilities with heterogeneous probability weighting (2019)
  4. Optimal portfolio selection in a Value-at-Risk framework (2001)
  5. Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis (2002)
  6. Portfolio optimization with entropic value-at-risk (2019)
  7. An enhanced model for portfolio choice with SSD criteria: a constructive approach (2011)
  8. Augmented Lagrangian Methods for Solving Optimization Problems with Stochastic-Order Constraints (2016)
and 131 more
  1. Optimization Problems with Second Order Stochastic Dominance Constraints: Duality, Compact Formulations, and Cut Generation Methods (2008)
  2. Portfolio optimization with stochastic dominance constraints (2006)
  3. Inverse stochastic dominance constraints and rank dependent expected utility theory (2006)
  4. Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints (2004)
  5. Optimization with Stochastic Dominance Constraints (2003)
  6. Portfolio Optimization with Expectile and Omega Functions (2019)
  7. Optimization of conditional value-at-risk (2000)
  8. Mean-Expectile Portfolio Selection (2021)
  9. Continuous-time mean–risk portfolio selection (2005)
  10. Dynamic Portfolio Choice When Risk Is Measured by Weighted V a R (2015)
  11. Adjusted Expected Shortfall (2022)
  12. Short Communication: Minimal Quantile Functions Subject to Stochastic Dominance Constraints (2022)
  13. A NOTE ON THE QUANTILE FORMULATION (2016) — link
  14. On the Neyman–Pearson problem for law-invariant risk measures and robust utility functionals (2004)
  15. Optimal and robust contracts for a risk-constrained principal (2009)
  16. BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME (2008) — link
  17. PORTFOLIO CHOICE VIA QUANTILES (2011) — link
  18. Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints (2006)
  19. Expected Utility Maximization with Stochastic Dominance Constraints in Complete Markets (2021) — link
  20. Risk management with weighted VaR (2018)
  21. A RROW– D EBREU EQUILIBRIA FOR RANK-DEPENDENT UTILITIES (2016)
  22. Optimization by Vector Space Methods (1969)
  23. Measure Theory (Vol. 2) (2007)
  24. Infinite Dimensional Analysis: A Hitchhiker’s Guide (2006)
  25. Stochastic Orders (2007)
  26. Optimal Control from Theory to Computer Programs (2003)
  27. A new characterization of comonotonicity and its application in behavioral finance (2014)
  28. Markowitz’s mean-variance asset-liability management with regime switching: A time-consistent approach (2013)
  29. Investment-consumption with regime-switching discount rates (2014)
  30. A method for determining whether parameters in aggregative models are structural (1988)
  31. Stock Returns, Expected Returns, and Real Activity (1990)
  32. Stock returns, asymmetric volatility, risk aversion, and business cycle: some new evidence (2008)
  33. The Endogenous Determination of Time Preference (1997)
  34. HARA frontiers of optimal portfolios in stochastic markets (2012)
  35. Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach (2007)
  36. Portfolio optimization in a regime-switching market with derivatives (2014)
  37. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle (1989)
  38. Analytical and Numerical Methods for Volterra Equations (1985) — link
  39. Nearly-optimal asset allocation in hybrid stock investment models (2004)
  40. American options with regime switching (2002)
  41. EXPLICIT SOLUTIONS OF CONSUMPTION-INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHING (2009)
  42. On the optimal dividend strategy in a regime-switching diffusion model (2012)
  43. Optimal dividend distribution under Markov regime switching (2012)
  44. Consumption–investment strategies with non-exponential discounting and logarithmic utility (2014)
  45. TIME-INCONSISTENT OPTIMAL CONTROL PROBLEM WITH RANDOM COEFFICIENTS AND STOCHASTIC EQUILIBRIUM HJB EQUATION (2015)
  46. Mean–Variance Portfolio Optimization with State-Dependent Risk Aversion (2014)
  47. Dynamic mean-variance asset allocation (2010)
  48. Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model (2003)
  49. Partial differential equations of parabolic type (1964)
  50. Well-posedness and regularity of backward stochastic Volterra integral equations (2008)
  51. General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations (2003)
  52. A Numerical scheme for BSDE s (2004)
  53. Backward Stochastic Differential Equations in Finance (1997)
  54. Time-inconsistent stochastic linear-quadratic control (2012)
  55. UTILITY MAXIMIZATION IN INCOMPLETE MARKETS (2005)
  56. Some empirical evidence on dynamic inconsistency (1981)
  57. Picoeconomics (1992)
  58. Anomalies in intertemporal choice: evidence and an interpretation (1992)
  59. On second-best national saving and game-equilibrium growth (1968)
  60. Golden eggs and hyperbolic discounting (1997)
  61. Ramsey meets Laibson in the neoclassical growth model (1999)
  62. On the existence of a consistent course of action when tastes are changing (1973)
  63. Consistent planning (1968)
  64. Consistent plans (1980)
  65. On time-inconsistent stochastic control in continuous time (2017)
  66. Being serious about non-commitment: subgame perfect equilibrium in continuous time (2006)
  67. Investment and consumption without commitment (2008)
  68. Lifetime portfolio selection under uncertainty: The continuous-time case (1969)
  69. Optimum consumption and portfolio rules in a continuous-time model (1971)
  70. Explicit Solution of a General Consumption/Investment Problem (1986)
  71. MARTINGALE AND DUALITY METHODS FOR UTILITY MAXIMIZATION IN AN INCOMPLETE MARKET (1991)
  72. Consumption and Portfolio Policies with incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case (1991)
  73. Methods of Mathematical Finance (1998)
  74. Myopia and inconsistency in dynamic utility maximization (1955)
  75. Time-Consistent Portfolio Management (2012)
  76. Non-constant discounting in finite horizon: The free terminal time case (2009)
  77. Consumption and portfolio rules for time-inconsistent investors (2010)
  78. Optimal portfolio and consumption decisions for a “small investor” on a finite horizon (1987)
  79. Quadratic BSDE s driven by a continuous martingale and applications to the utility maximization problem (2009)
  80. Adapted solution of a backward stochastic differential equation (1990)
  81. OPTIMAL CONSUMPTION AND INVESTMENT IN INCOMPLETE MARKETS WITH GENERAL CONSTRAINTS (2011)
  82. A deterministic linear quadratic time-inconsistent optimal control problem (2011)
  83. Deterministic time-inconsistent optimal control problems - An essential cooperative approach (2012)
  84. Time-inconsistent optimal control problems and the equilibrium HJB equation (2012)
  85. Quadratic hedging and mean-variance portfolio selection with random parameters in an incomplete market (2004)
  86. BSDE s with stochastic Lipschitz condition and quadratic PDE s in H ilbert spaces (2008)
  87. Minimization of risks in pension funding by means of contributions and portfolio selection (2001)
  88. Mean-variance portfolio and contribution selection in stochastic pension funding (2008)
  89. Optimal investment decisions with a liability: The case of defined benefit pension plans (2006) — link
  90. Funding and investment decisions in a stochastic defined benefit pension plan with several levels of labor-income earnings (2008)
  91. Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates (2010)
  92. Optimal risk management in defined benefit stochastic pension funds (2004)
  93. Mean-variance optimization problems for an accumulation phase in a defined benefit plan (2008)
  94. Stochastic investment returns and contribution rate risk in a defined benefit pension scheme (1997)
  95. Contribution and solvency risk in a defined benefit pension scheme (2000)
  96. Portfolio selection (1952)
  97. Continuous-time mean-variance portfolio selection: A stochastic LQ framework (2000)
  98. Optimal dynamic portfolio selection: Multi-period mean-variance formulation (2000)
  99. Optimal pension management in a stochastic framework (2004)
  100. An Introduction to Pension Schemes (1986)
  101. Stochastic pension fund control in the presence of Poisson jumps (2007)
  102. Defined benefit pension schemes: funding for ongoing security (1993)
  103. Dynamic approaches to pension funding (1994)
  104. Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time (2000)
  105. Pension funding incorporating downside risks (2003)
  106. The Semimartingale Dynamics and Generator of a Continuous Time Semi- M arkov Chain (2020) — link
  107. Optimal contributions in a defined benefit pension scheme with stochastic new entrants (2005)
  108. On the control of defined-benefit pension plans (2006)
  109. LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS — TIME-CONSISTENT SOLUTIONS (2017)
  110. Time-consistent mean-variance portfolio selection in discrete and continuous time (2013)
  111. Fundamentals of Convex Analysis (2001)
  112. Equilibrium for Time-Inconsistent Stochastic Linear–Quadratic Control under Constraint (2017)
  113. Time-Consistent Mean-Variance Asset-Liability Management with Random Coefficients (2017)
  114. Time-Inconsistent Stochastic Linear–Quadratic Control: Characterization and Uniqueness of Equilibrium (2017) — link
  115. Optimal investment strategies and risk measures in defined contribution pension schemes (2002)
  116. A BSDE approach to risk-based asset allocation of pension funds with regime switching (2012)
  117. Optimal management and in ation protection for defined contribution pension plans (2007)
  118. Optimal dynamic asset allocation strategy for ELA scheme of DC pension plan during the distribution phase (2013)
  119. Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans (2006)
  120. Lifetime investment and consumption using a defined-contribution pension scheme (2012)
  121. Self-control and saving for retirement (1998)
  122. Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model (2013)
  123. ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDE s WITH PERTURBATION SCHEME (2012)
  124. Stochastic Finance: an Introduction in Discrete Time (2016)
  125. Convexity and Optimization in Banach Spaces (2012)
  126. Repeated Games (2015)
  127. Real Analysis for Graduate Students (2013)
  128. Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition (2005)
  129. Convex Optimization in Normed Spaces Theory, Methods and Examples (2015)
  130. Behavioral Mean-Variance Portfolio Selection (2018)
  131. An Introduction to Optimal Control Problems in Life Sciences and Economics: From Mathematical Models to Numerical Simulation with MATLAB (2011)

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