This paper addresses the retirement income planning problem from the perspective of the four main building blocks of retirement income: state pension, mortality credits, investment strategies, and drawdown schedules. We detail how these building blocks interact to form a retiree's overall retirement income portfolio, and what trade-offs and interactions must be considered. We find that while access to each building block increases the retiree's certainty equivalent consumption, the most substantial contributor to this increase is from utilization of the mortality credit building block (i.e., annuities).

This study explores the economics of culling decisions in cow-calf operations in the Southern U.S. with a novel application of a dynamic mathematical programing model. The results provide an optimal culling strategy under the base model and a range of optimal strategies that vary with respect to different components such as fertility probabilities, prices, replacement costs, and pregnancy checking. The results suggest that producers should cull all cows that are older than age 10 and cows that fail to calve once they reach the age of 7. The sensitivity analysis underlines the impact of market conditions, replacement costs, and pregnancy check use on the optimal culling decisions.

This study relies on a linear programming model to estimate welfare ratios in Spain between 1600 and 1800. This method is used to find the food basket that guaranteed the intake of basic nutrients at the lowest cost. The estimates show that working families in Toledo had higher welfare ratios than in those in Barcelona. In addition, the welfare ratios of Spain were always below those of London and Amsterdam. The divergence between Northern Europe and Spain started before the Industrial Revolution and increased over time.

Reinsurers may default when they have to pay large claims to insurers but are unable to fulfill their obligations due to various reasons such as catastrophic events, underwriting losses, inadequate capitalization, or financial mismanagement. This paper studies the problem of optimal reinsurance design from the perspectives of both the insurer and reinsurer when the insurer faces the potential default risk of the reinsurer. If the insurer aims to minimize the convex distortion risk measure of his retained loss, we prove the optimality of a stop-loss treaty when the promised ceded loss function is charged by the expected value premium principle and the reinsurer offers partial recovery in the event of default. For any fixed premium loading set by the reinsurer, we then derive the explicit expressions of optimal deductible levels for three special distortion functions, including the TVaR, Gini, and PH transform distortion functions. Under these three explicit distortion risk measures adopted by the insurer, we seek the optimal safety loading for the reinsurer by maximizing her net profit where the reserve capital is determined by the TVaR measure and the cost is governed by the expectation. This procedure ultimately leads to the Bowley solution between the insurer and the reinsurer. We provide several numerical examples to illustrate the theoretical findings. Sensitivity analyses demonstrate how different settings of default probability, recovery rate, and safety loading affect the optimal deductible values. Simulation studies are also implemented to analyze the effects induced by the default probability and recovery rate on the Bowley solution.

We investigate whether a benchmark and non-constant risk aversion affect the probability density distribution of optimal wealth at retirement. We maximize the expected utility of the ratio of pension wealth at retirement to an inflation-indexed benchmark. Together with a threshold and a lower bound, we are able to generate closed-form solutions. We find that this non-constant risk aversion type of utility could shift the probability density distribution of optimal wealth more towards the benchmark, and that the probability of achieving a certain percentage of the desired benchmark could be increased. The probability density distribution generated under constant relative risk aversion (CRRA) risk preference is more widely spread along the benchmark.

In this paper, we explore how to design the optimal insurance contracts when the insured faces insurable, counterparty, and additive background risk simultaneously. The target is to minimize the mean-variance of the insured’s loss. By utilizing the calculus of variations, an implicit characterization of the optimal ceded loss function is given. An explicit structure of the optimal ceded loss function is also provided by making full use of its implicit characterization. We further derive a much simpler solution when these three kinds of risk have some special dependence structures. Finally, we give a numerical example to illustrate our results.

This study examines the economic performance of rainfed cropping systems endemic to the Southern Great Plains under weed competition. Cropping systems include tilled and no-till wheat-fallow, wheat-soybean, and wheat-sorghum rotations. Net returns from systems are compared under different levels of weed pressure. Producers operating over longer planning horizons would choose to double-crop regardless of the tillage method used and weed pressure level. Producers operating under shorter planning horizons would implement wheat-fallow systems when weed pressure is high and double crop when weed pressure is low.

This paper considers variable annuity (VA) contracts embedded with guaranteed minimum accumulation benefit (GMAB) riders when policyholder’s proceeds are taxed upon early surrender or maturity. These contracts promise the return of the premium paid by the policyholder, or a higher rolled-up value, at the end of the investment period. A partial differential equation valuation framework which exploits the numerical method of lines is used to determine fair fees that render the policyholder and insurer breakeven. Two taxation regimes are considered: one where capital gains are allowed to offset losses and a second where gains do not offset losses. Most insurance providers highlight the tax-deferred features of VA contracts. We show that the regime under which the insured is taxed significantly impacts prices. If losses are allowed to offset gains then this enhances the market, increasing the policyholder’s willingness to participate in the market compared to the case when losses are not allowed to offset gains. With fair fees from the policyholder’s perspective, we show that the net profit is generally positive for insurance companies offering the contract as a naked option without any hedge. We also show how investment policy, as reflected in the Sharpe ratio, impacts and interacts with policyholder persistency.

This paper studies dynamic reinsurance contracting and competition problems under model ambiguity in a reinsurance market with one primary insurer and n reinsurers, who apply the variance premium principle and who are distinguished by their levels of ambiguity aversion. The insurer negotiates reinsurance policies with all reinsurers simultaneously, which leads to a reinsurance tree structure with full competition among the reinsurers. We model the reinsurance contracting problems between the insurer and reinsurers by Stackelberg differential games and the competition among the reinsurers by a non-cooperative Nash game. We derive equilibrium strategies in semi-closed form for all the companies, whose objective is to maximize their expected surpluses penalized by a squared-error divergence term that measures their ambiguity. We find that, in equilibrium, the insurer purchases a positive amount of proportional reinsurance from each reinsurer. We further show that the insurer always prefers the tree structure to the chain structure, in which the risk of the insurer is shared sequentially among all reinsurers.

Policies designed to control greenhouse gases imply domestic tradeoffs and international externalities, which lead to both domestic and international conflicts, influencing their feasibility and implementations. Our paper investigates two quantitative aspects within this debate. We intend to quantify the impact of: (a) the internalization of international externalities; and (b) the damage associated with a short-term view of climate policies. In this respect, we adopt the innovative (in this field) idea of model predictive control to formalize moving-horizon policy strategies and, thus, to build counterfactuals characterized by a different horizon for all policymakers.

The Pasture, Rangeland, Forage (PRF) insurance program is aimed to assist producers to manage the risk of forage loss due to the lack of precipitation. However, limited attention has been given to understanding the implications of policyholders’ coverage selection decisions. In this study, three alternative risk-efficient portfolio selection strategies are assessed in to the context of the PRF program. Proposed methods consider all the decision parameters and program restrictions, and they highlighted the underlying relationships between expected revenue, risk, and choice of the coverage parameters. Selection strategies are illustrated by examining the optimal coverage for a grid in South Texas.

We study the optimal investment strategy to minimize the probability of lifetime ruin under a general mortality hazard rate. We explore the error between the minimum probability of lifetime ruin and the achieved probability of lifetime ruin if one follows a simple investment strategy inspired by earlier work in this area. We also include numerical examples to illustrate the estimation. We show that the nearly optimal probability of lifetime ruin under the simplified investment strategy is quite close to the original minimum probability of lifetime ruin under reasonable parameter values.

Fed cattle profitability is determined by complicated dynamic processes of body growth, carcass development, and seasonal prices. A structural model is constructed to contend with all these dynamic processes to predict optimal market timing. Informed simulations are conducted and compared to those observed in the data, as well as to a previous model ignoring the evolution of carcass value. The results indicate that significant improvements to profitability are attainable with the new method. The results also indicate the opportunity cost of not accounting for carcass value, even with error, is more severe than when these dynamics are ignored.

We construct investment glide paths for a retirement plan using both traditional asset classes and deferred annuities (DAs). The glide paths are approximated by averaging the asset proportions of stochastic optimal investment solutions. The objective function consists of power utility in terms of secured retirement income from purchased DAs, as well as a bequest that can be withdrawn before retirement. Compared with conventional glide paths and investment strategies, our DA-enhanced glide paths provide the investor with higher welfare gains, more efficient investment portfolios and more responsive retirement income patterns and bequest levels to different fee structures and personal preferences.

Target benefit (TB) plans that incorporate intergenerational risk sharing have been demonstrated to be welfare improving over the long term. However, there has been little discussion of the short-term benefits for members in a defined benefit (DB) plan that is transitioning to TB. In this paper, we adopt a two-step approach that is designed to ensure the long-term sustainability of the new plan, without unduly sacrificing the benefit security of current retirees. We propose a cohort-based transition plan for reducing intergenerational inequity. Our study is based on simulations using an economic scenario generator with some theoretical results under simplified settings.

This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.

Bonus-malus systems (BMSs) are widely used in actuarial sciences. These systems are applied by insurance companies to distinguish the policyholders by their risks. The most known application of BMS is in automobile third-party liability insurance. In BMS, there are several classes, and the premium of a policyholder depends on the class he/she is assigned to. The classification of policyholders over the periods of the insurance depends on the transition rules. In general, optimization of these systems involves the calculation of an appropriate premium scale considering the number of classes and transition rules as external parameters. Usually, the stationary distribution is used in the optimization process. In this article, we present a mixed integer linear programming (MILP) formulation for determining the premium scale and the transition rules. We present two versions of the model, one with the calculation of stationary probabilities and another with the consideration of multiple periods of the insurance. Furthermore, numerical examples will also be given to demonstrate that the MILP technique is suitable for handling existing BMSs.

Defined contribution (DC) pension plans have been gaining ground in the last 10–20 years as the preferred system for many countries and other agencies, both private and public. The central question for a DC plan is how to invest in order to reach the participant's retirement goals. Given the financial illiteracy of the general population, it is common to offer a default policy for members who do not actively make investment choices. Using data from the Chilean system, we discuss an investment model with fixed contribution rates and compare the results with the existing default policy under multiple objectives. Our results indicate that the Chilean default policy has good overall performance, but specific closed-loop policies have a higher probability of achieving desired retirement goals and can reduce the expected shortfall at retirement.

Pricing ultra-long-dated pension liabilities under the market-consistent valuation is challenged by the scarcity of the long-term market instruments that match or exceed the terms of pension liabilities. We develop a robust self-financing hedging strategy which adopts a min–max expected shortfall hedging criterion to replicate the long-dated liabilities for agents who fear parameter misspecification. We introduce a backward robust least squares Monte Carlo method to solve this dynamic robust optimization problem. We find that both naive and robust optimal portfolios depend on the hedging horizon and the current funding ratio. The robust policy suggests taking more risk when the current funding ratio is low. The yield curve constructed by the robust dynamic hedging portfolio is always lower than the naive one but is higher than the model-based yield curve in a low-rate environment.

We examine the investment performance of Chilean pension funds during their multi-fund period (2003–17). Using tradable asset class benchmarks, we extend Sharpe's (1992) return-based style analysis by explicitly considering regulatory restrictions and currency hedging. We find that despite the significant differences between pension fund manager returns, they are statistically similar to our style benchmarks for all fund types. Furthermore, accounting for currency hedging improves the accuracy of the replicating portfolios and the selection return estimates. Our results have policy implications for investment regulation of pension systems with similar characteristics to the Chilean one.