This paper proposes a multi-state model of both functional disability and health status in the presence of systematic trend and uncertainty. We classify each individual observation along two dimensions: health status (other than disability) and disability and use the multi-state latent factor intensity (MLFI) model to estimate the transitions rates. The model is then used to calculate (healthy) life expectancy and price a variety of insurance products. We illustrate the importance of various factors and quantify the potential losses from model misspecification. Our results suggest that insurers should pay great attention to health status, trend, and systematic uncertainty in disability/mortality modeling and insurance pricing. We also find that integrating long-term care (LTC) insurance with life annuity can help to reduce the systematic uncertainties.

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This article studies the optimal portfolio selection of expected utility-maximizing investors who must also manage their market-risk exposures. The risk is measured by a so-called weighted value-at-risk (WVaR) risk measure, which is a generalization of both value-at-risk (VaR) and expected shortfall (ES). The feasibility, well-posedness, and existence of the optimal solution are examined. We obtain the optimal solution (when it exists) and show how risk measures change asset allocation patterns. In particular, we characterize three classes of risk measures: the first class will lead to models that do not admit an optimal solution, the second class can give rise to endogenous portfolio insurance, and the third class, which includes VaR and ES, two popular regulatory risk measures, will allow economic agents to engage in "regulatory capital arbitrage," incurring larger losses when losses occur. K E Y W O R D Sexpected shortfall, portfolio insurance, portfolio selection, regulatory capital arbitrage, risk measure, value-at-risk, weighted value-at-risk 1020