arXiv subjects

Mogens Steffensen

Publications and source records attributed to Mogens Steffensen.

8 recordsLinked to original sources

arXiv2025

When Indemnity Insurance Fails: Parametric Coverage under Binding Budget and Risk Constraints

In high-risk environments, traditional indemnity insurance is often unaffordable or ineffective, despite its well-known optimality under expected utility. We compare excess-of-loss indemnity insurance with parametric insurance within a common mean-variance framework, allowing for fixed costs, heterogeneous premium loadings, and binding budget constraints. Motivated by the disaster insurance and risk-sharing literature, we show that, once these realistic frictions are introduced, parametric insurance can yield higher welfare for risk-averse individuals, even under the same utility objective and without relying on behavioral assumptions. The welfare advantage arises precisely when indemnity insurance becomes impractical (particularly when households face binding premium budgets), and disappears once both contracts are unconstrained. Our results help reconcile classical insurance theory with the growing use of parametric risk transfer in high-risk settings, and rationalize the interest in hybrid designs that combine both indemnity and parametric elements.

econ.GN↗

arXiv2025

Equilibrium investment under dynamic preference uncertainty

We study a continuous-time portfolio choice problem for an investor whose state-dependent preferences are determined by an exogenous factor that evolves as an It\^o diffusion process. Since risk attitudes at the end of the investment horizon are uncertain, terminal wealth is evaluated under a set of utility functions corresponding to all possible future preference states. These utilities are first converted into certainty equivalents at their respective levels of terminal risk aversion and then (nonlinearly) aggregated over the conditional distribution of future states, yielding an inherently time-inconsistent optimization criterion. We approach this problem by developing a general equilibrium framework for such state-dependent preferences and characterizing subgame-perfect equilibrium investment policies through an extended Hamilton-Jacobi-Bellman system. This system gives rise to a coupled nonlinear partial integro-differential equation for the value functions associated with each state. We then specialize the model to a tractable constant relative risk aversion specification in which the preference factor follows an arithmetic Brownian motion. In this setting, the equilibrium policy admits a semi-explicit representation that decomposes into a standard myopic demand and a novel preference-hedging component that captures incentives to hedge against anticipated changes in risk aversion. Numerical experiments illustrate how features of the preference dynamics -- most notably the drift of the preference process and the correlation between preference shocks and asset returns -- jointly determine the sign and magnitude of the hedging demand and the evolution of the equilibrium risky investment over time.

q-fin.MF↗

arXiv2024

Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time

In intertemporal settings, the multiattribute utility theory of Kihlstrom and Mirman suggests the application of a concave transform of the lifetime utility index. This construction, while allowing time and risk attitudes to be separated, leads to dynamically inconsistent preferences. We address this issue in a game-theoretic sense by formalizing an equilibrium control theory for continuous-time Markov processes. In these terms, we describe the equilibrium strategy and value function as the solution of an extended Hamilton-Jacobi-Bellman system of partial differential equations. We verify that (the solution of) this system is a sufficient condition for an equilibrium and examine some of its novel features. A consumption-investment problem for an agent with CRRA-CES utility showcases our approach.

q-fin.MF↗

arXiv2022

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.

math.OC↗

arXiv2022

Optimal reinsurance design under solvency constraints

We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled "down" via reinsurance, rather than "up" via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the $\mathbb{P}$ and $\mathbb{Q}$ measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated.

math.OC↗

arXiv2019

Matrix calculations for inhomogeneous Markov reward processes, with applications to life insurance and point processes

A multi--state life insurance model is naturally described in terms of the intensity matrix of an underlying (time--inhomogeneous) Markov process which describes the dynamics for the states of an insured person. Between and at transitions, benefits and premiums are paid, defining a payment process, and the technical reserve is defined as the present value of all future payments of the contract. Classical methods for finding the reserve and higher order moments involve the solution of certain differential equations (Thiele and Hattendorf, respectively). In this paper we present an alternative matrix--oriented approach based on general reward considerations for Markov jump processes. The matrix approach provides a general framework for effortlessly setting up general and even complex multi--state models, where moments of all orders are then expressed explicitly in terms of so--called product integrals (matrix--exponentials) of certain matrices. As Thiele and Hattendorf type of theorems can be retrieved immediately from the matrix formulae, this methods also provides a quick and transparent approach to proving these classical results. Methods for obtaining distributions and related properties of interest (e.g. quantiles or survival functions) of the future payments are presented from both a theoretical and practical point of view (via Laplace transforms and methods involving orthogonal polynomials).

math.PR↗

arXiv2015

Optimal Portfolio Liquidation and Dynamic Mean-variance Criterion

In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered mean-variance subject at any point in time. We get explicit trading strategies in the basic model and when random pricing signals are incorporated. When we consider stochastic liquidity and volatility, we construct a generalized HJB equation under general assumptions for the parameters. We obtain an explicit solution in stochastic volatility model with a given structure supported by empirical studies.

q-fin.TR↗

arXiv2014

Reserve-Dependent Surrender

We study the modelling and valuation of surrender and other behavioural options in life insurance and pension. We place ourselves in between the two extremes of completely arbitrary intervention and optimal intervention by the policyholder. We present a method that is based on differential equations and that can be used to approximate contract values when policyholders exhibit optimal behaviour. This presentation includes a specification of sufficient conditions for both consistency of the model and convergence of the contract values. When not going to the limit in the approximation we obtain a technique for balancing off arbitrary and optimal behaviour in a simple, intuitive way. This leads to our suggestions for intervention models where one single parameter reflects the extent of rationality among policyholders. In a series of numerical examples we illustrate the impact of the rationality parameter on the contract values.

q-fin.MF↗