We investigate the optimal asset allocation and repayment strategy of an agricultural loan under a guaranteed repayment condition in a continuous-time setting. We propose two forms of the problem: an analytically solvable “separable” problem and a more realistic “nominal” problem that is investigated numerically. In the numerical study, we calibrate our model to publicly available farm data and explore various forms of repayment structures. While the widely used constant repayment structure has a surprisingly outstanding performance, we also design two repayment structures for the nominal problem that perform quite well.

This paper examines an insurer’s optimal asset allocation and reinsurance policies. The financial market framework includes one risk-free and one risky asset. The insurer has two business lines, where the ordinary claim process is modeled by a compound Poisson process and catastrophic claims follow a compound dynamic contagion process. The dynamic contagion process, which is a generalization of the externally exciting Cox process with shot-noise intensity and the self-exciting Hawkes process, is enhanced by accommodating the dependency structure between the magnitude of contribution to intensity after initial events for catastrophic insurance products and its claim/loss size. We also consider the dependency structure between the positive effect on the intensity and the negative crashes on the risky financial asset when initial events occur. Our objective is to maximize the insurer’s expected utility of terminal surplus. We construct the extended Hamilton–Jacobi–Bellman (HJB) equation using dynamic programming principles to derive an explicit optimal reinsurance policy for ordinary claims. We further develop an iterative scheme for solving the value function and the optimal asset allocation policy and the reinsurance policy for catastrophic claims numerically, providing a rigorous convergence proof. Finally, we present numerical examples to demonstrate the impact of key parameters.

This paper studies the dynamic relationship between economic growth, pollution, and government intervention. To do so, we develop a model that links pollution to the economy’s productive capacity, thereby capturing the feedback loops between economic activity, environmental degradation, and fiscal policy intervention. The model incorporates a pollution-sensitive damage function, taxes, and government spending while analyzing economic growth under different levels of government intervention. Therefore, the main paper’s contributions reveal that economies can achieve favorable outcomes with low or moderate government intervention, and that our results underscore the vital role of pollution mitigation policy in dynamically balancing economic growth with environmental sustainability.

Climate change, partly driven by rising emissions, has damaging and often irreversible impacts on entire economies. In this context, production processes play a crucial role, as they affect the level of pollution, causing environmental degradation, and affecting human health. Sustainable production methods and stricter environmental regulations can help mitigate these effects. However, their effectiveness depends on many factors as, for instance, the attitude towards greenery by firms and their convenience in breaking the rules. In the present work, we propose a dynamic framework to describe how and in which measure the production processes influence the environmental quality, considering the presence of non-compliant firms and the attitude toward greenery. We obtain a 3D piecewise-smooth dynamical system describing the evolution of the fraction of polluting firms, the monitoring level by the State, and the environmental quality over time. By analyzing the effects on environmental quality of the environmental regulation enforcement for different greenery propensities, we show that: (1) if the propensity for greenery is high, the system will converge towards a good equilibrium, that is, with high environmental quality and absence of dishonest companies; (2) if the propensity for greenery is at an intermediate level, the system may converge towards good or bad equilibria; (3) if the propensity for greenery is low, further internal attractors may emerge.

In this paper, we study a two-period optimal insurance problem for a policyholder with mean-variance preferences who purchases proportional insurance at the beginning of each period. The insurance premium is calculated by a variance premium principle with a risk loading that depends on the policyholder’s claim history. We derive the time-consistent optimal insurance strategy in closed form and the optimal constant precommitment strategy in semiclosed form. For the optimal general precommitment strategy, we obtain the solution for the second period semi-explicitly and, then, the solution for the first period numerically via an efficient algorithm. Furthermore, we compare the three types of optimal strategies, highlighting their differences, and we examine the impact of the key model parameters on the optimal strategies and value functions.

The bonus-malus system (BMS) is a widely recognized and commonly employed risk management tool. A well-designed BMS can match expected insurance payments with estimated claims even in a diverse group of risks. Although there has been abundant research on improving bonus-malus (BM) systems, one important aspect has been overlooked: the stationary probability of a BMS satisfies the monotone likelihood ratio property. The monotone likelihood ratio for stationary probabilities allows us to better understand how riskier policyholders are more likely to remain in higher premium categories, while less risky policyholders are more likely to move toward lower premiums. This study establishes this property for BMSs that are described by an ergodic Markov chain with one possible claim and a transition rule +1/-d. We derive this result from the linear recurrences that characterize the stationary distribution; this represents a novel analytical approach in this domain. We also illustrate the practical implications of our findings: in the BM design problem, the premium scale is automatically monotonic.

Within a new Keynesian model of monetary policy with both backward- and forward-looking variables, we investigate the impact of risk aversion by assuming that the central bank is endowed with recursive preferences à la Hansen and Sargent (Hansen and Sargent, 1995). We establish that, since in this model inflation and output are forward-looking, under discretion the optimal policy is found by solving two distinct fixed-point problems: the former pertains to the central bank’s optimization exercise, the latter to the identification of the equilibrium expectations of the forward-looking variables. We show that, in the presence of forward-looking variables, the optimal policy differs from the robust policy chosen by a central bank endowed with quadratic preferences and subject to Knightian uncertainty, confuting the equivalence established by Hansen and Sargent (2008) when only backward-looking variables enter into the laws of motion regulating the dynamics of the economic system. Through our analysis we show: i) how a risk-averse central bank selects a more aggressive policy than one furnished with the standard preferences of a canonical DSGE model; ii) that the “divine coincidence” established within traditional linear-quadratic formulations between inflation and output stabilization no longer holds.

This study introduces a data-driven benchmarking method to assess the relative price and profit efficiencies of cattle auction sales. Transaction inefficiencies represent the divergence between observed sales and their corresponding maximum feasible value. Data envelopment analysis is used to assess market efficiencies and to identify the optimal array of animal characteristics based on peer comparisons. In Texas, about half of the evaluated transactions were inefficient. Furthermore, by modifying some of the observed attributes, sales prices could increase by 23% and profits improve by 74%. Efficiency results can be used to develop effective value-added management practices and educational programs.

Microplastic pollution from plastic fragments accumulating in agricultural fields threatens the world’s most productive soils and environmental sustainability. This is the first paper to address the challenge of developing a dynamic economic model to analyze the adoption of soil-biodegradable plastic mulches (BDMs) as a sustainable alternative to conventional polyethylene mulches. The model considers the trade-off between BDM degradation rates and agricultural production, seeking to balance the cost of BDMs and the cost of waste disposal. We consider both private and social perspectives under deterministic and stochastic environments. Our findings suggest that BDMs can significantly decrease long-term plastic pollution from single-use plastics in agriculture. For example, increasing landfill tipping fees incentivizes Washington State tomato growers to optimally adopt BDMs with a 61% degradation rate and to till used BDMs into the soil, reducing plastic waste accumulation in landfills. The study highlights the role of economic incentives, such as landfill fees, corrective taxes and the role of risk aversion, in promoting BDM adoption and curbing plastic pollution. The framework presented here offers valuable insights for policymakers and stakeholders seeking to foster sustainable agricultural practices and mitigate global plastic pollution.

Risk was incorporated into monetary aggregation over thirty-five years ago, using a stochastic version of the workhorse money-in-the-utility-function model. Nevertheless, the mathematical foundations of this stochastic model remain shaky. To firm the foundations, this paper employs richer probability concepts than Borel-measurability, enabling me to prove the existence of a well-behaved solution and to derive stochastic Euler equations. This measurability approach is less common in economics, possibly because the derivation of stochastic Euler equations is new. Importantly, the problem’s economics are not restricted by the approach. The results provide firm footing for the growing monetary aggregation under risk literature, which integrates monetary and finance theory. As crypto-currencies and stable coins garner attention, solidifying the foundations of risky money becomes more critical. The method also supports deriving stochastic Euler equations for any dynamic economics problem that features contemporaneous uncertainty about prices, including asset pricing models like capital asset pricing models and stochastic consumer choice models.

This work shows that direct combustion of cotton gin waste (CGW) at cotton gins can profitably generate electricity. Many bioenergy processing centres emphasise very large-scale operations, which require a large and stable bio-stock supply that is not always available. Similarly, a small biorefinery processing gin trash at a cotton gin must wrestle with the high volatility of cotton yields and price variation in cotton and electricity. Fortunately, the smaller scale allows these risks to be somewhat countervailing. Low cotton yields allow the limited gin trash available to be applied to the highest peak electricity prices in winter. Similarly, high yields with low cotton prices generate revenue from power generation throughout high winter electric prices.

To assess the profitability of an onsite power plant requires high-resolution data. We utilise hourly electricity price data from 2010 to 2021 in West Texas and obtain a small data array of 15 years of gin trash at a medium-sized gin. Prior analyses have had neither. We leverage limited CGW data to better leverage generous electricity price data by generating a Bayesian distribution for CGW. We simulate 10,000 annual CGW outcomes and electricity prices. Using engineering parameters for combustion efficiency, we show the expected internal rates of return of 19–22% for a 1 MWe and a 2 MWe plant at a small gin. Simulations then compare economic returns to the variance of those returns, which allows the analyst to present to investors a frontier of stochastic dominant return outcomes (risk-returns trade-off) for plants of different sizes at different sized gins.

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.