Duality Theory

On Cost-Sensitive Distributionally Robust Log-Optimal Portfolio ArXiv ID: 2410.23536 “View on arXiv” Authors: Unknown Abstract This paper addresses a novel \emph{“cost-sensitive”} distributionally robust log-optimal portfolio problem, where the investor faces \emph{“ambiguous”} return distributions, and a general convex transaction cost model is incorporated. The uncertainty in the return distribution is quantified using the \emph{“Wasserstein”} metric, which captures distributional ambiguity. We establish conditions that ensure robustly survivable trades for all distributions in the Wasserstein ball under convex transaction costs. By leveraging duality theory, we approximate the infinite-dimensional distributionally robust optimization problem with a finite convex program, enabling computational tractability for mid-sized portfolios. Empirical studies using S&P 500 data validate our theoretical framework: without transaction costs, the optimal portfolio converges to an equal-weighted allocation, while with transaction costs, the portfolio shifts slightly towards the risk-free asset, reflecting the trade-off between cost considerations and optimal allocation. ...

Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning ArXiv ID: 2312.02943 “View on arXiv” Authors: Unknown Abstract This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent’s option to choose when to acquire life insurance for bequest purposes. We examine two scenarios: one with a fixed bequest amount and another with a controlled bequest amount. Applying duality theory and addressing free-boundary problems, we analytically solve both cases, and provide explicit expressions for value functions and optimal strategies in both cases. In the first scenario, where the bequest amount is fixed, distinct outcomes emerge based on different levels of risk aversion parameter $γ$: (i) the optimal time for life insurance purchase occurs when the agent’s wealth surpasses a critical threshold if $γ\in (0,1)$, or (ii) life insurance should be acquired immediately if $γ>1$. In contrast, in the second scenario with a controlled bequest amount, regardless of $γ$ values, immediate life insurance purchase proves to be optimal. Finally, we extend the analysis to consider a scenario in which the individual earmarks part of her initial wealth for inheritance, where a critical wealth threshold consistently emerges. ...