A dynamic programming approach to constrained portfolios

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption

Portfolio Optimization and Mortgage Choice

This paper studies the optimal mortgage choice of an investor in a simple bond market with a stochastic interest rate and access to term life insurance. The study is based on advances in stochastic control theory, which provides analytical solutions to portfolio problems with a stochastic interest rate. We derive the optimal portfolio of a mortgagor in a simple framework and formulate stylized versions of mortgage products offered in the market today. This allows us to analyze the optimal investment strategy in terms of optimal mortgage choice. We conclude that certain extreme investors optimally choose either a traditional fixed rate mortgage or an adjustable rate mortgage, while investors with moderate risk aversion and income prefer a mix of the two. By matching specific investor characteristics to existing mortgage products, our study provides a better understanding of the complex and yet restricted mortgage choice faced by many household investors. In addition, the simple analytical framework enables a detailed analysis of how changes to market, income and preference parameters affect the optimal mortgage choice

Continuing Risks

Risks will soon celebrate its tenth anniversary. We would like to take this opportunity to thank all authors, readers, and reviewers of the past decade. Ten years ago, Risks was the new journal in the class; a journal that entered a competitive classroom with enough self-confidence to believe that it had a role to play there. This new journal immediately became the rebellious student in the class. Risks stood up against conventions and challenged the power of habits. Risks had, and still has, some unique features in terms of both its format and content that make it stand out from its peers

Stable Dividends under Linear-Quadratic Optimization

The optimization criterion for dividends from a risky business is most often formalized in terms of the expected present value of future dividends. That criterion disregards a potential, explicit demand for stability of dividends. In particular, within actuarial risk theory, maximization of future dividends have been intensively studied as the so-called de Finetti problem. However, there the optimal strategies typically become so-called barrier strategies. These are far from stable and suboptimal affine dividend strategies have therefore received attention recently. In contrast, in the class of linear-quadratic problems a demand for stability if explicitly stressed. These have most often been studied in diffusion models different from the actuarial risk models. We bridge the gap between these patterns of thinking by deriving optimal affine dividend strategies under a linear-quadratic criterion for a general L\'evy process. We characterize the value function by the Hamilton-Jacobi-Bellman equation, solve it, and compare the objective and the optimal controls to the classical objective of maximizing expected present value of future dividends. Thereby we provide a framework within which stability of dividends from a risky business, as e.g. in classical risk theory, is explicitly demanded and explicitly obtained

Systemic virus infection results in CD8 T cell recruitment to the retina in the absence of local virus infection

During recent years, evidence has emerged that immune privileged sites such as the CNS and the retina may be more integrated in the systemic response to infection than was previously believed. In line with this, it was recently shown that a systemic acute virus infection leads to infiltration of CD8 T cells in the brains of immunocompetent mice. In this study, we extend these findings to the neurological tissue of the eye, namely the retina. We show that an acute systemic virus infection in mice leads to a transient CD8 T cell infiltration in the retina that is not directed by virus infection inside the retina. CD8 T cells were found throughout the retinal tissue, and had a high expression of CXCR6 and CXCR3, as also reported for tissue residing CD8 T cells in the lung and liver. We also show that the pigment epithelium lining the retina expresses CXCL16 (the ligand for CXCR6) similar to epithelial cells of the lung. Thus, our results suggest that the retina undergoes immune surveillance during a systemic infection, and that this surveillance appears to be directed by mechanisms similar to those described for non-privileged tissues

The Management of Decumulation Risks in a Defined Contribution Pension Plan

The aim of the paper is to lay the theoretical foundations for the construction of a flexible tool that can be used by pensioners to find optimal investment and consumption choices in the distribution phase of a defined contribution pension plan. The investment/consumption plan is adopted until the time of compulsory annuitization, taking into account the possibility of earlier death. The effect of the bequest motive and the desire to buy a higher annuity than the one purchasable at retirement are included in the objective function. The mathematical tools provided by dynamic programming techniques are applied to find closed-form solutions: numerical examples are also presented. In the model, the tradeoff between the different desires of the individual regarding consumption and final annuity can be dealt with by choosing appropriate weights for these factors in the setting of the problem. Conclusions are twofold. First, we find that there is a natural time-varying target for the size of the fund, which acts as a sort of safety level for the needs of the pensioner. Second, the personal preferences of the pensioner can be translated into optimal choices, which in turn affect the distribution of the consumption path and of the final annuity