Stochastic Returns Research Articles

Emerging cost-time Pareto front for diffusion with stochastic return

Abstract Resetting, in which a system is regularly returned to a given state after a fixed or random duration, has become a useful strategy to optimize the search performance of a system. While earlier theoretical frameworks focused on instantaneous resetting, wherein the system is directly teleported to a given state, there is a growing interest in physical resetting mechanisms that involve a finite return time. However employing such a mechanism involves cost and the effect of this cost on the search time remains largely unexplored. Yet answering this is important in order to design cost-efficient resetting strategies. Motivated from this, we present a thermodynamic analysis of a diffusing particle whose position is intermittently reset to a specific site by employing a stochastic return protocol with external confining trap. We show for a family of potentials U R ( x ) ∼ | x | m with m > 0, it is possible to find optimal potential shape that minimises the expected first-passage time for a given value of the thermodynamic cost, i.e. mean work. By varying this value, we then obtain the Pareto optimal front, and demonstrate a trade-off relation between the first-passage time and the work done.

Asymptotics for Finite-Time Ruin Probabilities of a Dependent Bidimensional Risk Model with Stochastic Return and Subexponential Claims

The paper considers a bidimensional continuous-time risk model with subexponential claims and Brownian perturbations, in which the price processes of the investment portfolio of the two lines of business are two geometric Lévy processes and the two lines of business share a common claim-number process, which is a renewal counting process. The paper mainly considers the claims of each line of business having a dependence structure. When the claims have subexponential distributions, the asymptotics of the finite-time ruin probabilities ψand(x1,x2;T) and ψsim(x1,x2;T) have been obtained. When the distributions of claims belong to the intersection of long-tailed and dominatedly varying-tailed distribution classes, the asymptotics of the finite-time ruin probability ψor(x1,x2;T) is given.

Finite-time ruin probability of a risk model with perturbation and subexponential main claims and by-claims

The paper considers a nonstandard risk model with stochastic return and perturbation, in which the price process of the investment portfolio is described as a geometric Lévy process and each main claim may induce a delayed by-claim. When the main claims and by-claims have subexponential distributions, we obtain some asymptotic estimations of the finite-time ruin probability.

Increasing convex order of capital allocation with dependent assets under threshold model

In this manuscript, we consider a risk-preference investor allocating some amount of capital to the dependent risky asset, where the responding asset will occur default if the stochastic return is less than some predetermined threshold. Then, we present sufficient conditions of the increasing convex order on capital allocation with dependent risky assets when the stochastic return is right tail weakly stochastic arrangement increasing. Finally, some numerical examples are given as illustrations.

Uniform asymptotics for finite-time ruin probabilities of a bidimensional compound risk model with stochastic returns

Consider a continuous-time bidimensional compound risk model with stochastic returns, where an insurance company operates two lines of business at the same time and is allowed to invest its wealth into financial assets. In this model, each accident may cause a random number of heavy-tailed claims and the claim sizes from the same line of business are upper tail asymptotically independent, while the accident arrival processes from different lines of business are arbitrarily dependent. Under some moment conditions on the accident arrival processes, some uniform asymptotic formulae for finite-time ruin probabilities are established.

Asymptotics for sum-ruin probabilities of a bidimensional risk model with heavy-tailed claims and stochastic returns

This paper considers a bidimensional risk model with geometric Lévy price processes and dependent heavy-tailed claims, where the two claim-number processes generated by the two different lines of business are almost arbitrarily dependent. When the distributions of the claims are subexponential with a positive lower Matuszewska index, an asymptotic formula for the finite-time sum-ruin probability is derived, which has a more transparent form when the distributions of the claims are regularly-varying-tailed and the two claim-number processes are homogeneous Poisson processes. Some simulation studies are conducted to verify the accuracy and sensitivity of the asymptotic result by employing the crude Monte Carlo method.

Asymptotic ruin probabilities for a two-dimensional risk model with dependent claims and stochastic return

We consider a continuous-time two-dimensional risk model, in which the claims from the two lines of insurance businesses satisfy an extensive asymptotic independence structure and the stochastic return is driven by a geometric Lévy process. Under a mild technical condition regarding the Laplace exponent of the Lévy process, we obtain explicit asymptotic expansions for both finite-time and infinite-time ruin probabilities when the claim sizes have regularly varying distributions.

A Stochastic Markov Chain for Estimating New Entrants into Professional Pension Funds

This paper presents a stochastic Markov chain model for estimating new entrants into professional orders and their related pension funds. The model considers the interactions between demographic, socio-economic and regulatory variables. The intuition behind it is that, in the medium term, trends in academic education can anticipate changes in the job market and preferences for highly skilled professions. Similarly, in the long term, fertility trends can anticipate the number of future young adults, thus influencing the overall occupational structure of employment. The model has been formalized mathematically and successfully validated by backtesting over historical data. The model’s predictions have been compared with the observed data of new entrants into the Italian order of chartered accountants (CNDCEC) between 2012 and 2021. The related professional pension fund (CNPADC) has also been analyzed under the additional assumption of stochastic returns with an evaluation of the impact of future new chartered accountants on its demographic and financial evolution between 2020 and 2070.

Dynamic Amnesty Programs

A regulator faces a stream of agents engaged in crimes with stochastic returns. The regulator designs an amnesty program, committing to a time path of punishments for criminals who report their crimes. In an optimal program, time variation in the returns from crime can generate time variation in the generosity of amnesty. I construct an optimal time path and show that it exhibits amnesty cycles. Amnesty becomes increasingly generous over time until it hits a bound, after which the cycle resets. Agents engaged in high return crime report at the end of each cycle, while agents engaged in low return crime report always. (JEL D82, D86, K42)

Work fluctuations for diffusion dynamics submitted to stochastic return

Returning a system to a desired state under a force field involves a thermodynamic cost, i.e. work. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to determine the work distribution for returning a system facilitated by a confining potential with its minimum at the restart location. The general strategy, based on average over resetting pathways, constitutes a robust method to gain access to the statistical information of observables from resetting systems. We exploit paradigmatic setups, where explicit computations are attainable, to illustrate the theory. Numerical simulations validate our theoretical predictions. For some of these examples, a non-trivial behavior of the work fluctuations opens a door to optimization problems. Specifically, work fluctuations can be minimized by an appropriate tuning of the return rate.

Single item periodic review inventory control with sales dependent stochastic return flows

Retailers have to deal with increasing levels of product returns as the shares of e-commerce sales soars. With this increase, it is no longer feasible to dispatch returned products to outlets or landfills, hence retailers must re-evaluate them both to maximize profit and to minimize their environmental impact. Our objective is to study a retailer’s optimal inventory control policy under product returns to maximize expected profit which is the sales revenue minus the procurement, backorder, holding, and salvage costs incurred in a finite horizon. We model a period’s returns to be stochastically dependent on the previous period’s sales quantity. Using dynamic programming formulation, we solve for the optimal periodic review inventory policy and provide structural results on the optimal policy of the final period. Through numerical studies, we show that incorporating detailed sales-dependent returns could increase a retailer’s expected profit by 23%. Ignoring this dependency in determining the optimal inventory policy results with increased order frequency, higher levels of backorders and more leftovers which could eventually end up in a landfill, but above all could lead to a significant overestimation of the resulting profit.

Benefits of Preconditioning Cattle under Stochastic Feedlot Performance

AbstractPreconditioning cattle, a management practice of preparing cattle for feedlots as well as following a vaccination protocol for common diseases, has been shown to add value to cattle by reducing disease incidence and severity, yet it is not universally adopted. We estimated the benefits to a beef system of preconditioning weaned calves versus not preconditioning under stochastic returns. Purchasing preconditioned calves makes economic sense, but market efficiency requires complete information of the health status of the cattle, feedlot performance, along with the right market mechanisms, which may not be available in all markets.

The finite-time ruin probability of a risk model with stochastic return and subexponential claim sizes*

Consider a renewal risk model with stochastic return and stochastic perturbation, where the price process of the investment portfolio is a geometric Lévy process. When the claim sizes have a dependence structure, we derive the asymptotics of the finite-time ruin probability for all subexponential claim sizes. Particularly, when the claim sizes come from a subclass of the subexponential distribution class, the finite-time ruin probability has been estimated for claim sizes with a general dependence structure.

Uniform asymptotics for ruin probabilities of a delayed renewal risk model with one-sided linear dependence and stochastic returns

In this article, we consider a renewal risk model with by-claims, where the price process of the investment portfolio follows an exponential Lévy process. We further assume that the main claim is a one-sided linear process and there exists a certain dependence structure between the innovations and by-claims. In the presence of heavy tails, we obtain a series of uniform formulas in finite and infinite intervals. In order to better describe the obtained results, we carry on the numerical simulations.

Seismic Resilience Assessment Strategy for Social and Sustainability Impact Evaluation on Transportation Road Network: A Seismic Liquefaction-Induced Damage Application

Transport networks play a critical role for living communities, as they facilitate the exchange of people and goods and foster economic growth. Improving their resilience against seismic hazards, among which liquefaction is by far one of the most significant and complex, is consistent with most of the Sustainable Development Goals pinpointed by the United Nations’ Agenda. In this paper, an original methodological framework, combining innovative Geo-statistical approaches to analyze soil properties, prediction models for soil liquefaction, and calibrated transport demand models providing the social and economic cost associated with seismic-induced road damages and closures within a renewed Geographical Information Systems (GIS) workspace, is proposed. In particular, based on traditional risk assessment evaluation, an innovative approach to evaluate the exposure in terms of economic loss due to lack of accessibility is presented. The methodology is applied to a district area in northern Italy that underwent a recent seismic event that caused several soil liquefaction phenomena. Results provided by a sensitivity analysis on a stochastic (return period) basis are derived: as the seismic intensity increases, the total social costs increase, but the trend of the rates due to traffic delays and the loss of accessibility are irregular. Although further simulation scenarios need to be undertaken, the proposed methodology seems to provide an effective planning tool to evaluate preventive strategies aimed at improving the resilience of transport networks against liquefaction risk.

Uniform asymptotics for a nonstandard compound renewal risk model with dependence structures and stochastic return on investments

Consider a nonstandard compound renewal risk model with stochastic return on investments, where the price process of investment portfolio is modeled as an exponential Lévy process. In the presence of heavy tails and dependence structures among modeling components, we study the uniform asymptotics of the tail probability of stochastic discounted aggregate claims and the finite-time ruin probability for all time varying in a relevant finite or infinite interval.

Uniform asymptotics for ruin probabilities of multidimensional risk models with stochastic returns and regular variation claims

Consider a multidimensional discrete-time risk model in terms of some dependence structure. For the case of multivariate regularly varying claims, we study the asymptotic behavior of the ruin probabilities determined by some ruin sets. The estimates hold uniformly for all time horizons. Then we focus on a ruin set that allows partial capital transfers. As an application, the optimal allocation of the initial reserve is obtained. Some numerical simulations are presented to illustrate the results.

The finite-time ruin probability of a risk model with a general counting process and stochastic return

<p style='text-indent:20px;'>This paper considers a general risk model with stochastic return and a Brownian perturbation, where the claim arrival process is a general counting process and the price process of the investment portfolio is expressed as a geometric Lévy process. When the claim sizes are pairwise strong quasi-asymptotically independent random variables with heavy-tailed distributions, the asymptotics of the finite-time ruin probability of this risk model have been obtained.</p>

A simheuristic algorithm for the portfolio optimization problem with random returns and noisy covariances

The goal of the portfolio optimization problem is to minimize risk for an expected portfolio return by allocating weights to included assets. As the pool of investable assets grows, and additional constraints are imposed, the problem becomes NP-hard. Thus, metaheuristics are commonly employed for solving large instances of rich versions. However, metaheuristics do not fully account for random returns and noisy covariances, which renders them unrealistic in the presence of heightened uncertainty in financial markets. This paper aims to close this gap by proposing a simulation–optimization approach – specifically, a simheuristic algorithm that integrates a variable neighborhood search metaheuristic with Monte Carlo simulation – to deal with stochastic returns and noisy covariances modeled as random variables. Computational experiments performed on a well-established benchmark instance illustrate the advantages of our methodology and analyze how the solutions change in response to a varying degree of randomness, minimum required return, and probability of obtaining a return exceeding an investor-defined threshold.

A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

The non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. The estimation of the model is difficult, since the unobservable surplus demand is a time-varying stochastic variable in the return equation, and the market liquidity arises both in the mean term and in the variance term of the return equation in the MM model. A fast and efficient Markov Chain Monte Carlo (MCMC) approach based on an efficient simulation smoother algorithm and an acceptance-rejection Metropolis–Hastings algorithm is designed to estimate the non-linear MM model. Since the simulation smoother algorithm makes use of the band diagonal structure and positive definition of Hessian matrix of the logarithmic density, it can quickly draw the market liquidity. In addition, we discuss the MM model with Student-t heavy tail distribution that can be utilized to address the presence of outliers in typical financial time series. Using the presented modeling method to make analysis of daily income of the S&P 500 index through the point forecast and the density forecast, we find clear support for time-varying volatility, volatility feedback effect, market microstructure theory, and Student-t heavy tails in the financial time series. Through this method, one can use the estimated market liquidity and surplus demand which is much smoother than the strong stochastic return process to assist the transaction decision making in the financial market.