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Structuring a viable pension plan is a problem that arises in the study of financial contracts pricing and bears special importance these days. Deterministic pension models often rely on projections that are based on several assumptions…
This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer's surplus follows the diffusion approximation of…
We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption…
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
The generic case of pensions fund that it is not sufficiently auto financed and it is thoroughly maintained with an external financing effort is considered in this chapter. To represent the unrestricted reserves value process of this kind…
In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors. We give a numerical algorithm to compute the optimal investment-consumption strategy for an infinite…
This paper is concerned with a time-inconsistent recursive stochastic control problems where the forward state process is constrained through an additional recursive utility system. By adapting the Ekeland variational principle, necessary…
This paper studies a continuous-time optimal portfolio selection problem in the complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor concerns about the terminal…
In this paper, we work in the framework of the Merton problem but we impose a drawdown constraint on the consumption process. This means that consumption can never fall below a fixed proportion of the running maximum of past consumption. In…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
In this paper, we undertake an investigation into the utility maximization problem faced by an economic agent who possesses the option to switch jobs, within a scenario featuring the presence of a mandatory retirement date. The agent needs…
In order to deal with the aging problem, pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET…
We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of…
The Australian Government uses the means-test as a way of managing the pension budget. Changes in Age Pension policy impose difficulties in retirement modelling due to policy risk, but any major changes tend to be `grandfathered' meaning…
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the…
We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness results for the value functions of the portfolio/consumption choice problem. As an…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…