Time-consistency Problem Research Articles

A non-zero-sum investment and reinsurance game between two mean–variance insurers with dynamic CVaR constraints

This paper is devoted to investigating a non-zero-sum game between two competing insurers. The insurers can diversify their insurance risks by purchasing proportional reinsurance and investing their collected premiums into a financial market composed of one risk-free asset and one stock. The reinsurance premiums charged by the reinsurer follow the generalized mean–variance premium principle. Moreover, the dynamic CVaR constraints are incorporated in the game problem to control risks. With the dynamic mean–variance objective, we introduce two forward deterministic auxiliary processes to represent the expectations of the insurers’ wealth processes and transform the original time inconsistent game problem into a standard time consistent game problem with two state variables for each insurer. By adopting the dynamic programming principle and the Lagrange duality method, we derive the Nash equilibrium investment–reinsurance strategies for the two insurers. Finally, the effects of several important model parameters on the optimal policies are analyzed by numerical examples.

Cooperative differential games with the utility function switched at a random time moment

This paper describes a differential game of $n$ persons in which the utility functions of the players have a hybrid form, namely, they are changed at a random moment in time. With the help of integration in parts, the form of the payoff functional is simplified. For the cooperative scenario the problem of time-consistency of the optimality principle chosen by the players is studied and a solution is proposed in the form of an adapted imputation distribution procedure. The differential investment game is considered as an example.

Optimal Time-Consistent Government Debt Maturity, Fiscal Policy, and Default

Abstract I develop a tractable model to study the optimal debt maturity structure and fiscal policy in an environment with incomplete markets, lack of commitment, and opportunity to default by the government. I show that the Lucas and Stokey time-consistency result can be extended to environments with an opportunity of outright default. The maturity is used to resolve the time-consistency problem. I show that if both risk-free interest rates and risk premiums can be manipulated, then the optimal maturity structure tends to have a decaying profile: The government issues debt at all maturity dates, but the distribution of payments over time is skewed toward the short end. The model allows for numerical characterization of the optimal maturity structure of debt with an arbitrarily large number of maturities. Debt maturity data across countries are consistent with model predictions.

Balancing Before and After: Treasury Market Reform Proposals and the Connections Between Ex-Ante and Ex-Post Liquidity Tools

<ns3:p>This paper develops a simple framework that helps to draw out some of the potential connections between ex-ante liquidity risk management tools such as liquidity requirements or mandatory fees and ex-post liquidity tools such as a lender of last resort. A central message of this analysis is that policy actions that expand the lender of last resort function so as to better address periods of financial distress are likely to be most effective when accompanied by regulations or other mechanisms that encourage socially-responsible ex-ante liquidity risk management on the part of financial firms. Regulation in the form of a liquidity coverage requirement can be helpful in moving private sector outcomes toward a social optimum. A mandatory fee schedule also emerges as a potentially very useful tool. The structure of the optimal fee schedule depends on both the scale of volatile liabilities and the extent of “liquidity coverage” maintained to cover potential funding shortfalls. Both liquidity requirements and mandatory fees can help to address a form of time consistency problem in connection with the provision of ex-post liquidity support through a lender of last resort. The framework also provides some potentially useful benchmarks in evaluating the distribution of liquidity risks across different classes of financial firms.</ns3:p>

Optimal Monetary Policy with Heterogeneous Agents in Iran (1989-2017): A Model Based on Time Consistency Problem

Policy rules as one of the most acceptable methods in monetary policies are among the significant characteristics of researches about policymaking. A policy rule states how the policy tools should react to changes in economic situations. Understanding the tools and criteria of monetary policies such as changes in target inflation, changes in relative weights of prices stability and employment, and its effect on different sections of society including households and economic firms can help economic policymakers to increase the effectiveness of monetary policies. This paper studies the time consistency and structure of optimal monetary policy from the viewpoint of public sector finance concerning the heterogeneous behavior of economic agents in form of keeping liquidity and nominal assets in Iran. The study utilizes time-series data quarterly from Q1 1989 to Q4 2017. A new Keynesian dynamic stochastic general equilibrium (DSGE) models have been developed for monetary policy analysis in open economies. Results show that the redistribution effect of monetary policy leads to breakage of the link between time consistency and high inflation; a characteristic that belongs to optimal monetary and fiscal policies.

Hyperbolic discounting in an intergenerational model with altruistic parents

Hyperbolic utility discounting has emerged as a leading alternative to exponential discounting because it can explain time-inconsistent behaviors. Intuitively, hyperbolic discounting should play a crucial role in intergenerational models characterized by intertemporal trade-offs. In this paper, we incorporate hyperbolic discounting into a dynamic model in which parents are altruistic towards their children. Agents live for four periods and choose levels of consumption, fertility, investment in their children’s human capital, and bequests to maximize discounted utility. In the steady state, hyperbolic discounting decreases fertility, increases human capital investment, and shifts consumption towards younger ages. These effects are more pronounced in the time-consistent problem (in which agents cannot commit to a course of action) than in the commitment problem, which can be interpreted as realized and intended actions, respectively. The preference-based discrepancy between intended fertility and realized fertility has important implications for the empirical literature that compares the two.

Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process

We consider an optimal investment and risk control problem for an insurer under the mean–variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem related to the original MV problem, and obtain the optimal strategy and the value function to the new problem in closed-form. We compare our formulation and optimal strategy to those under the precommitment and game-theoretic framework. Numerical studies show that, when the financial market is negatively correlated with the risk process, optimal investment may involve short selling the risky asset and, if that happens, a less risk averse insurer short sells more risky asset.

The collaborative consistent vehicle routing problem with workload balance

The rising competition in the logistics sector forces companies to be more economically efficient. One of the major sources of inefficiency is the incomplete usage of available resources, such as vehicles’ capacities. Mechanism that allow to better exploit such resources by enabling carrier collaborations are on the rise. Our study examines a centrally organized multi-period collaborative vehicle routing problem, where carriers can exchange customers who have to be serviced on a regular basis. Collaborations, where carriers serve frequent customers, are supposed to face the problem of (i) time consistency in terms of visiting time, and of (ii) service consistency. The latter ensures that customers are visited by the same collaboration partner throughout the whole planning horizon. Additionally, carriers might only be willing to enter a collaboration if a minimum market share can be guaranteed. In order to take all these issues into account, we introduce the collaborative vehicle routing problem with time and service consistency and workload balance. The mathematical model including several valid inequalities is presented. In a computational study, we solve small-sized instances to optimality. In order to tackle larger instances, we propose an efficient and effective matheuristic and an iterated local search algorithm. We show that both methods reach near optimal solutions within very short computational times. Managerial insights on the cost of imposing time and service consistency as well as workload balancing constraints are presented and discussed. We show that, according to our computational study, consistency constraints can be imposed for almost no additional cost, while workload balancing constraints do not have any negative effect on the total collaboration profit. This is a meaningful insight and might be a strong argument for carriers to enter collaborations.

Optimally Rewarding Countries for Reducing Fossil Fuel Supply and Demand: A Time Consistency Problem

Consider a world with complete information in which a global institution receives an exogenous flow of funding which it can use to curb fossil fuels by rewarding countries for reducing supply or reducing demand. I show that the ex ante optimal path of reward payment schemes is not time consistent. The global institution will in the future have incentives to partly shift its budget from the supply side towards the demand side relative to what it initially announced. If the global institution cannot commit at all then a version of the Weak Green Paradox always arises. However, I show that the Strong Green Paradox is highly implausible. I argue that the the time consistency problem will also arise to some extent in the more realistic setting with endogenous funding if there is a separate institution for each of the approaches and donors can flexibly earmark their flows of contributions. I discuss potential approaches to mitigating the time consistency problem.

Optimal time-consistent reinsurance strategies for mean-variance insurers under thinning dependence structure

This paper considers an optimal time-consistent proportional reinsurance problem with constraints on the strategies under the mean-variance criterion for an insurer. It is assumed that the surplus process is described by a compound Poisson risk model with dependent classes of insurance business named thinning-dependence structure, in which the stochastic sources related to claim occurrence are classified into different groups, and that each group may cause a claim in each insurance class with a certain probability. By solving the extended Hamilton-Jacobi-Bellman equation within the game theoretic framework, not only explicit expressions of the optimal strategies and value function are obtained for but closed-form expressions of optimal results are derived for by the method of dimension reduction. Moreover, some numerical examples are presented to illustrate the effects of parameters on the optimal strategies as well as the economic interpretation behind.

EMPIRICAL EVIDENCE ON THE IMPACT OF MONETARY POLICY ON NATIONAL ECONOMIC GROWTH

This article discusses empirical evidence of----imonetary -----ipolicy's impact----ion national----ieconomic growth----iin the decade 2010-2019. This article is analyzed using a regression analysis tool. This article concludes that 1) the interest rate (BI Rate) has----ian---iimpact rate----ion national----ieconomic---igrowth---iin----ithe decade 2010-2019 of only 7 percent. Impact-----iof US $----iexchange----irate---ion----ithe domestic----ieconomic----igrowth---iof only 90 percent 3) Impact of the amount of money in circulation on the national economic growth of only 76.8 percent, 4) Impact----iof----iinflation----irate----ion----ithe domestic economic growth of only 4.3 percent 5) impact of total investment in national economic growth is only 60.8 percent. Thus-----ithe----imain-----iobjective-----iof-----imonetary-----ipolicy is more emphasis-----ion-----iprice-----istability. With the first consideration, with output determined by long-term economic capacity, all systems that encourage economic growth will create inflation so that it will not affect real economic growth. Second, the rational financial agent understands that policymakers' actions in supporting the economic growth that helps increase can lead to time consistency problems. Third, monetary policy influencing economic variables takes a long time and has a lag. Fourth, price stability can encourage creating a better economic climate because it will reduce costs from inflation

EMPIRICAL EVIDENCE ON THE IMPACT OF MONETARY POLICY ON NATIONAL ECONOMIC GROWTH

This article discusses empirical evidence of----imonetary -----ipolicy's impact----ion national----ieconomic growth----iin the decade 2010-2019. This article is analyzed using a regression analysis tool. This article concludes that 1) the interest rate (BI Rate) has----ian---iimpact rate----ion national----ieconomic---igrowth---iin----ithe decade 2010-2019 of only 7 percent. Impact-----iof US $----iexchange----irate---ion----ithe domestic----ieconomic----igrowth---iof only 90 percent 3) Impact of the amount of money in circulation on the national economic growth of only 76.8 percent, 4) Impact----iof----iinflation----irate----ion----ithe domestic economic growth of only 4.3 percent 5) impact of total investment in national economic growth is only 60.8 percent. Thus-----ithe----imain-----iobjective-----iof-----imonetary-----ipolicy is more emphasis-----ion-----iprice-----istability. With the first consideration, with output determined by long-term economic capacity, all systems that encourage economic growth will create inflation so that it will not affect real economic growth. Second, the rational financial agent understands that policymakers' actions in supporting the economic growth that helps increase can lead to time consistency problems. Third, monetary policy influencing economic variables takes a long time and has a lag. Fourth, price stability can encourage creating a better economic climate because it will reduce costs from inflation

Committing to Decarbonize

Climate targets are key for focusing global efforts to limit anthropogenic climate change. Yet, they induce a time-consistency problem in that current decision makers set (ambitious) targets and leave costly abatement to future generations. We develop a reduced-form climate-economy integrated assessment model, and compare naive and sophisticated climate policies. We also differentiate between immediate and durable emission reduction measures. Our findings demonstrate that naive decision makers consistently weaken climate stabilization targets, resulting in an equilibrium that misses the initial proposal. Sophisticated decision makers foresee the weakened outcome, and invest more in durable abatement measures in order to incentivize future decision makers to continue emission reduction efforts. Our results indicate that effective climate policy goes beyond the carbon price; it also involves strategic selection of abatement measures.

A Cap-and-Trade Commitment Policy with Allowance Banking

We examine the planner’s dynamic regulation problem in an emission trading system (ETS) with allowance banking. The planner sets the emissions cap for the next period after the current period allowance market has cleared, but before knowing the next period’s abatement cost realization. This creates a time consistency problem when banking is possible. We examine two policies to overcome the consistency problem: a commitment solution and the Markov perfect solution. We show that the endogenous price floor generated by the banking demand becomes an integral feature of the two policies. Hence, they can be best described as hybrid policies that combine elements from emissions taxes and tradable allowances. This reveals new welfare implications that have an influence on instrument choice in the traditional prices versus quantities setup. We compare the expected welfare outcomes of four different policy instruments: the commitment policy, the Markov policy, a Pigouvian tax, and a no-banking ETS. We show that allowing banking can yield welfare gains compared to tax and quantity regulation, with or without commitment.

Reproducing the results in “Does the time-consistency problem explain the behavior of inflation in the United States?” using the Metropolis–Hastings algorithm

The study of Ireland (J Monet Econ 44:279–291, 1999) derives the restrictions imposed by Barro and Gordon’s theory of time-consistent monetary policy on a bivariate time-series model for US inflation and unemployment rate. The model is then estimated via maximum likelihood techniques using quarterly data from 1960q1 to 1997q2. In this study, we reproduce the central results of Ireland (1999) using the Metropolis–Hastings algorithm. Although we apply Bayesian instead of classical estimation, posterior parameter estimates are similar to maximum likelihood parameter estimates reported in Ireland (1999).

A non-exponential discounting time-inconsistent stochastic optimal control problem for jump-diffusion

In this paper, we study general time-inconsistent stochastic control models which are driven by a stochastic differential equation with random jumps. Specifically, the time-inconsistency arises from the presence of a non-exponential discount function in the objective functional. We consider equilibrium, instead of optimal, solution within the class of open-loop controls. We prove an equivalence relationship between our time-inconsistent problem and a time-consistent problem such that the equilibrium controls for the time-consistent problem coincide with the equilibrium controls for the time-inconsistent problem. We establish two general results which characterize the open-loop equilibrium controls. As special cases, a generalized Merton's portfolio problem and a linear-quadratic problem are discussed.

Strongly Time-Consistent Core in Differential Games with Discrete Distribution of Random Time Horizon

In this paper we investigate the problem of strong time-consistency of the core for a particular class of differential games with random time horizon, namely, it is assumed that there exists a set of probabilities of the end of the game at discrete time instants. A condition guaranteeing the strong time consistency of the core is presented.

Time-consistent mean-variance hedging of an illiquid asset with a cointegrated liquid asset

When a financial institution has a difficulty to close a position in an illiquid asset, a practical solution is to hedge the risk of the position with a related liquid asset. This may frequently occur in insurance institutions who diversify asset allocation by illiquid investment and face high transaction costs when try to close the illiquid asset position. A conventional approach constructs optimal hedging based on the correlation between the liquid and illiquid assets. We show, however, that ignoring the serial dependence through cointegration significantly reduces the hedging effectiveness. This paper investigates the time-consistent mean-variance optimal hedging using cointegration for the risk of a non-traded portfolio. Specifically, only the investment amount in the liquid asset is the control variable. The mathematical challenge stems on the derivation of the optimal equilibrium strategy when we have to deal with cointegration, illiquidity and time-inconsistency simultaneously. Using a stochastic differential game approach, we characterize the equilibrium hedging strategy from a system of partial differential equations that involves an HJB equation for the time-consistent problem with cointegration. Novel solutions to the equilibrium strategy and the efficient frontier are obtained in explicit closed-form formulas. The significance of cointegration in the corresponding hedging problem is evidenced with real empirical data.

Managing Capital Outflows with Limited Reserves

We analyze the optimal intervention policy for an emerging market central bank that wishes to stabilize the exchange rate during a capital outflow episode, but possesses limited reserves. We show that adding a non-negativity constraint on reserves onto a simple linear-quadratic framework generates a time consistency problem. A central bank with full commitment achieves a gradual depreciation to the pure-float level by promising sustained future intervention, such that reserves are exhausted after particularly adverse shocks. A central bank without commitment intervenes little, wishing to preserve some reserves forever, so it suffers a larger immediate depreciation and achieves lower welfare. For more persistent shocks, the time consistency problem is greater, and simple intervention rules can achieve welfare gains relative to discretion.

Time-consistent mean–variance proportional reinsurance and investment problem in a defaultable market

In this paper, we consider an optimal time-consistent reinsurance-investment problem incorporating a defaultable security for a mean–variance insurer under a constant elasticity of variance (CEV) model. In our model, the insurer’s surplus process is described by a jump-diffusion risk model, the insurer can purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset, a defaultable bond and a risky asset whose price process is assumed to follow a CEV model. Using a game theoretic approach, we establish the extended Hamilton–Jacobi–Bellman system for the post-default case and the pre-default case, respectively. Furthermore, we obtain the closed-from expressions for the time-consistent reinsurance-investment strategy and the corresponding value function in both cases. Finally, we provide numerical examples to illustrate the impacts of model parameters on the optimal time-consistent strategy.