We study Merton's expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters. Based on the entropy-regularization framework for general continuous-time RL formulated in Wang et al. (2020), we propose a recursive weighting scheme on exploration that endogenously discounts the current exploration reward by the past accumulative amount of exploration. Such a recursive regularization restores the optimality of Gaussian exploration. However, contrary to the existing results, the optimal Gaussian policy turns out to be biased in general, due to the interwinding needs for hedging and for exploration. We present an asymptotic analysis of the resulting errors to show how the level of exploration affects the learned policies. Furthermore, we establish a policy improvement theorem and design several RL algorithms to learn Merton's optimal strategies. At last, we carry out both simulation and empirical studies with a stochastic volatility environment to demonstrate the efficiency and robustness of the RL algorithms in comparison to the conventional plug-in method.

Goal-based wealth management (GBWM), also known as goal-based investing [1], is a relatively new class of approaches to wealth management that focus on attaining specific financial objectives (goals). As opposed to more traditional approaches to wealth management, in which the notion of expected profit and loss (PnL) plays a central role, GBWM revolves around maximizing the probability of goal attainment. Common investment goals include saving for college tuition, retirement, or purchasing a home. Recent years have seen an uptick in the popularity of GBWM [2], particularly through the use of target date funds (TDFs). TDFs, also known as life-cycle funds [3] or target-retirement funds, are mutual funds or exchange-traded funds that provide investors with an asset allocation aimed at fulfilling a target (goal) by a specified target date (e.g. a retirement date).

In this paper I explore the scaffolding of normative assumptions that supports Sabina Leonelli's implicit appeal to the values of epistemic integrity and the global public good that conjointly animate the ethos of responsible and sustainable data work in the context of COVID-19. Drawing primarily on the writings of sociologist Robert K. Merton, the thinkers of the Vienna Circle, and Charles Sanders Peirce, I make some of these assumptions explicit by telling a longer story about the evolution of social thinking about the normative structure of science from Merton's articulation of his well-known norms (those of universalism, communism, organized skepticism, and disinterestedness) to the present. I show that while Merton's norms and his intertwinement of these with the underlying mechanisms of democratic order provide us with an especially good starting point to explore and clarify the commitments and values of science, Leonelli's broader, more context-responsive, and more holistic vision of the epistemic integrity of data scientific understanding, and her discernment of the global and biospheric scope of its moral-practical reach, move beyond Merton's schema in ways that effectively draw upon important critiques. Stepping past Merton, I argue that a combination of situated universalism, methodological pluralism, strong objectivity, and unbounded communalism must guide the responsible and sustainable data work of the future.

"I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all." Chance appears to name a single, unitary thing. But its genealogy, its family history, turns out to be a tangled one. One way to understand its branching origins is to turn to literature: We may look, in turn, to two very different novels. Anton Chigurh, the antagonist of Cormac McCarthy's novel No Country for Old Men, forces his victims to guess the outcome of a coin toss, taking their life if they guess in error. That chance is entirely contained, not in Chigurh, but in the toss--in nature itself. This is one source of uncertainty.

However, implementing such a strategy requires combining the VFI framework with policy parameterization, rebalancing continually as assets prices fluctuate, the proposed ADP method enjoys complementary advantages and therefore will lead to high or even infinite transaction of low approximation errors from VFI and high computational costs. Since then researchers have tried to address this issue efficiency from policy parameterization. Briefly, by solving Merton's portfolio problem in the presence the components from VFI pave the way for effectively parameterizing of transaction costs. Thereinto, the proportional transaction a complex policy in a high-dimensional space; costs model, as a suitable model for brokerage commissions the components from policy parameterization provide a and bid-ask spread costs, typifies the common situation pathway to efficiently evaluating the strategy and bypassing for normal investors (Brandt 2010; Cvitanic 2001; the issue of error amplification.