This paper investigates the inverse problem of bi-revealed utilities in a defaultable universe, defined as a standard universe (represented by a filtration $\mathbb{F}$) perturbed by an exogenous defaultable time $\tau $. We assume that the standard universe does not take into account the possibility of the default, thus $\tau $ adds an additional source of risk. The defaultable universe is represented by the filtration $\mathbb{G}$ up to time $\tau $ ($\tau $ included), where $\mathbb{G}$ stands for the progressive enlargement of $\mathbb{F}$ by $\tau $. The basic assumption in force is that $\tau $ avoids $\mathbb{F}$ -stopping times. The bi-revealed problem consists in recovering a consistent dynamic utility from the observable characteristic of an agent. The general results on bi-revealed utilities, first given in a general and abstract framework, are translated in the defaultable $\mathbb{G}$ -universe and then are interpreted in the $\mathbb{F}$ -universe. The decomposition of $\mathbb{G}$ -adapted processes ${X}^{\mathbb{G}}$ provides an interpretation of a $\mathbb{G}$ -characteristic ${X}_{\tau }^{\mathbb{G}}$ stopped at $\tau $ as a reserve process. Thanks to the characterization of $\mathbb{G}$ -martingales stopped at $\tau $ in terms of $\mathbb{F}$ -martingales, we establish a correspondence between $\mathbb{G}$ -bi-revealed utilities from characteristic and $\mathbb{F}$ -bi-revealed pair of utilities from characteristic and reserves. In a financial framework, characteristic can be interpreted as wealth and reserves as consumption. This result sheds a new light on the consumption in utility criterion: the consumption process can be interpreted as a certain quantity of wealth, or reserves, that are accumulated for the financing of losses at the default time.

This paper proposes and investigates an optimal pair investment/pension policy for a pay-as-you-go (P A Y G) pension scheme. The social planner can invest in a buffer fund in order to guarantee a minimal pension amount. The model aims at taking into account complex dynamic phenomena such as the demographic risk and its evolution over time, the time and age dependence of agents preferences, and financial risks. The preference criterion of the social planner is modeled by a consistent dynamic utility defined on a stochastic domain, which incorporates the heterogeneity of overlapping generations and its evolution over time. The preference criterion and the optimization problem also incorporate sustainability, adequacy and fairness constraints. The paper designs and solves the social planner’s dynamic decision criterion, and computes the optimal investment/pension policy in a general framework. A detailed analysis for the case of dynamic power utilities is provided.

We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity. Incompleteness stems from general investment constraints, while model uncertainty is represented by a convex and compact set of plausible model parameter processes. Following the max-min criteria in traditional (backward) robust control, we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes. We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies. Furthermore, we present additional results within the class of homothetic constant relative risk aversion (CRRA) processes. Within this class, we investigate the relationship between forward performance processes on wealth and those on consumption, establishing an interesting dominance through time.

We introduce a new type of robust forward criterion under model uncertainty, called the G -forward performance process, which extends the classical notion of forward performance process to the G -expectation framework. We then derive the representations of homothetic G -forward performance processes in a single stochastic factor model with uncertainty, building on the well-posedness of ergodic and infinite horizon backward stochastic differential equations driven by G -Brownian motion (G -BSDEs) with quadratic generators.

We introduce a new approach for optimal portfolio choice under model ambiguity by incorporating predictable forward preferences in the framework of Angoshtari et al. [2]. The investor reassesses and revises the model ambiguity set incrementally in time while, also, updating his risk preferences forward in time. This dynamic alignment of preferences and ambiguity updating results in time-consistent policies and provides a richer, more accurate learning setting. For each investment period, the investor solves a worst-case portfolio optimization over possible market models, which are represented via a Wasserstein neighborhood centered at a binomial distribution. Duality methods from Gao and Kleywegt [10]; Blanchet and Murthy [8] are used to solve the optimization problem over a suitable set of measures, yielding an explicit optimal portfolio in the linear case. We analyze the case of linear and quadratic utilities, and provide numerical results.