Optimal Tax Inspection Strategy

A game-theoretical model is constructed describing the interaction of tax inspectors with taxpayers. The models allows for tax evasion and bribing of inspectors. We find the primary and secondary audit probabilities that maximize the net tax revenue for various inspector hiring strategies. The comparative revenue statics is analyzed and the optimal hiring strategy is determined as a function of the model parameters.     

Optimal Tax Enforcement with Imperfect Tax Payers and Inspectors

A mathematical model of tax enforcement is analyzed for the case when the probability of detecting tax evasion depends on the inspector's efforts. Contrary to the case with fixed inspection costs, the optimal tax enforcement strategy does not fully eliminate tax evasion. We examine how tax payers' random mistakes and the inspectors' corruptibility affect the optimal tax enforcement mechanism. We show that, contrary to the model with fixed inspection costs, corruption among inspectors reduces the optimal tax revenue.     

Bioeconomic harvesting of a schooling fish species: A dynamic reaction model

This paper develops a mathematical model for growth and exploitation of a schooling fish species, using a realistic catchrate function and imposing a tax on the catch to control harvesting. Fishing effort is assumed to depend on the net revenue. The steady states of the system are determined and their local and global stability are discussed. Taking the tax as a control variable; the optimal harvest policy is formulated and solved as a control problem. The results are illustrated with the help of a numerical example.     

A mathematical model of optimal tax inspection

A game-theoretical model of tax inspection is considered. Stable forms of behavior of the entrepreneurs and the tax inspectors are identified as a function of the strategy adopted by the central tax service. An optimal central strategy is proposed, which maximizes the average tax revenue for given entrepreneur incomes.Translated from Programmno-apparatnye Sredstva i Matematicheskoe Obespechenie Vychislitel'nykh Sistem, pp. 168–181, 1994.     

财政腐败的宏观经济分析:一个理论框架

建立了一个考虑税收腐败和公共支出腐败的经济增长模型,从理论上探讨财政腐败行为及其影响.主要结论归纳:第一,财政腐败降低私人资本的回报率,使厂商的生产力下降,就整体而言阻碍了经济增长.第二,最优税率可能大于或小于Barro的最优税率,取决于征税效率和寻租引发的行政成本,第三,两种类型的公共支出隐含着不同程度的腐败机会,以...     

Symptotic estimates of insurance tariffs in the individual risk model

In the paper, asymptotic estimates of insurance tariffs that are least admissible for the insurer are obtained; the individual risk model and factorization model of an insurance claim for various distributions of insurance portfolio volume are considered. Supported by the Russian Humanitarian Scientific Foundation (grant No. 97-02-02235) and by the Russian Foundation for Fundamental Research (grant No. 93-01-00271). Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Tax-Adjusted Replacement Models

The 1984 UK Finance Act introduced changes in tax legislation with consequences for both capital and revenue expenditure on plant. The one- and two-cycle rent models for capital equipment replacement and the infinite-cycle discounted-cost model are extended here to incorporate the new tax features. A specific replacement problem is used as the basis of an analyis of the sensitivity of the optimal replacement period to parameters. Whilst all these models are consistently insensitive to the new tax legislation, there is no consistency across models with respect to which parameters dominate choice of optimal replacement period.     

Modelling profitability using survival combination scores

The paper presents the first empirical investigation of the relationship between present value of net revenue from a revolving credit account and times to default and to second purchase. The analysis is based on the data for a store card which is used to buy ‘white’ durable goods in Germany. It is demonstrated that there exists a relationship between the above given measures. It appears that there is a scope for improving profit if an application for a store card is assessed by using a model which estimates the revenue and includes the survival probability of default and the survival probability of second purchase (a survival combination model) rather than merely a static probability of default predicted by a logistic regression.     

Stable coexistence mediated by specialist harvesting in a two zooplankton–phytoplankton system

This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings.     

The effect of depreciation allowances on the timing of investment and government tax revenue

We develop a model of the behavior of a potential investor (under uncertainty and in a fiscal environment) who wishes to invest into a project in the real sector of an economy and faces a timing problem. We find an optimal solution within this model and examine the dependence of the tax revenue from the newly created firm on the depreciation policy. It is shown that there exists a domain in the space of the parameters of the investment project where both the tax revenue and the incentives can be increased by using the depreciation policy.     

Optimization methods in a nonhomogeneous periodic stochastic control model

A discrete-time stochastic optimal control model is considered. The traditional model assumes that all objects are homogeneous in time. However, in many applications some objects are time-dependent. In general, the optimization problem is apparently unsolvable in a nonhomogeneous model with an unbounded time horizon. If the transition function and the utility function are constrained to satisfy a natural periodicity condition, then the nonhomogeneous problem reduces to a homogeneous problem and becomes fully solvable. The objective of this study is to develop and generalize these results to a general constructive paradigm, which produces solution methods for both nonhomogeneous and homogeneous stochastic optimal control problems. The study has been partially supported by the Russian Foundation of Basic Research, grant No. 95-01-01137. Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 20–35, 1994.     

A framework for solving network revenue management problems with customer choice behavior

Revenue management is the process of understanding, anticipating and influencing consumer behavior in order to maximize revenue. Network revenue management models attempt to maximize revenue when customers buy bundles of multiple resources. The dependence among the resources in such cases is created by customer demand. Network revenue management can be formulated as a stochastic dynamic programming problem whose exact solution is computationally intractable. Solutions are based on approximations of various types. Customer choice behavior modeling has been gaining increasing attention in the revenue management. A framework for solving network revenue management problems with customer choice behavior is proposed. The modeling and solving framework is composed from three inter-related network structures: basic network model, Petri net, and neural net.     

基于社会福利最大化的油气资源税费研究

合理的油气资源税费能够引导企业优化开发决策,平衡当代与后代利益关系,实现跨期资源有效配置。从跨期油气资源最优分配的角度,通过最优控制理论构建寡头垄断市场中社会福利最大化和企业利润最大化目标下的油气资源开发决策模型,并以社会福利最大化目标下的资源开发决策为基准,研究从价、从量、储量三种不同形式的油气资源税费对资源开发决策的调节作用,研究发现:(1)征收从价税费,最优的从价税率为26.4%,政府既可以保障社会最优,还可以获得较多的税费收入;(2)征收从量税费,从量税率为1.77元/吨,政府可以保证社会福利最大化,但相比从价税费政府的税费收入较少;(3)征收储量税费,社会福利最大化下的储量税费为-0.13元/吨,也就是政府需向企业进行补贴才可以保证社会最优,会形成一定的财政压力。     

Lundberg’s risk process with tax

In this paper we extend the classical Cramér–Lundberg risk model by including tax payments. The considered tax rule is to pay a certain proportion of the premium income, whenever the portfolio is in a profitable situation. It is shown that the resulting survival probability is a power of the survival probability without tax. Furthermore, an explicit expression for the expected discounted total sum of tax payments until ruin according to this taxation rule is derived and the optimal starting level for taxation is determined. Finally, numerical illustrations of the results are given for the case of exponential claim amounts.     

Guaranteed bounds for insurance premium rates for the insurance portfolio of factorizable claims

In this paper, we obtain guaranteed upper bounds for the minimal possible insurance premium in the individual risk model with factorizable claims; we consider cases where the volume of the insurance portfolio is fixed and where that volume is distributed by the Poisson law. Supported by the Russian Foundation for Fundamental Research (grant No. 97-01-00271) and the Russian Humanitarian Science Foundation (grant No. 97-02-02235). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part III.     

On the convergence in law of almost all sums of independent random variables

The paper deals with sums of independent and identically distributed random variables defined on some probability space which are multiplied by random coefficients. These coefficients are the values of independent random variables defined on another probability space. We obtain conditions for the weak convergence of weighted sums, for almost all coefficients, to some infinitely divisible distribution. The limit distribution for these sums is found. Supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099). Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993.     

Reliability of a system with regular inspection times

A method of calculating upper and lower bounds of the reliability function and mean life time is proposed for a system subjected to regular inspections. With the help of minimal cut sets, a lower bound of the reliability function is obtained; the corresponding numerical procedure requires minor calculations. Supported in part by the Russian Foundation for Fundamental Research (grant No. 95-01-00023), the International Science Foundation and the Russian Government (grant J76100), and the EEC (grant INTAS-93-893). Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

Solving elliptical equations with high-contrast coefficients in an unbounded region

An approximation model is proposed for an elliptical equation with complex rapidly varying coefficients. An efficient numerical method is developed and implemented. A problem of geoelectricity requiring solution of an equation in this setting is investigated. This research was partially supported by the Russian Foundation for Basic Research (grant No. 96-05-64340) and by the Interuniversity Scientific Program “Russian Universities: Basic Research.” Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 37–45, 1998.     

Body forces equivalent to jumps of stresses and displacements in the Biot model of an anisotropic porous medium

Formulas for the body forces equivalent to given jumps of stresses and displacements in the anisotropic Biot model are obtained. Similarly to the case of elastic media, Betti's identity, the reciprocity relations, and the representation integrals for a porous media are derived first. The equivalent body forces are obtained by applying the representation integrals to a volume with surfaces of discontinuity. Some physical consequences are indicated, and examples of equivalent body forces for the isotropic Biot model are provided.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 33–44.The author wishes to express his sincere gratitude to V. M. Babich and L. A. Molotkov for helpful discussions. This work was supported in part by the Soros Foundation under grant A96-378 and the Russian Foundation for Basic Research under grant 96-05-65904.     

Dynamic bidding strategies in search-based advertising

Search-based advertising allows the advertisers to run special campaigns targeted to different groups of potential consumers at low costs. Google, Yahoo and Microsoft advertising programs allow the advertisers to bid for an ad position on the result page of a user’s query when the user searches for a keyword that the advertiser relates to its products or services. The expected revenue generated by the ad depends on the ad position, and the ad positions of the advertisers are concurrently determined after an instantaneous auction based on the bids of the advertisers. The advertisers are charged only when their ads are clicked by the users. To avoid excessive ad expenditures due to sudden surges in the keyword-search activities, each advertiser reserves a fixed finite daily budget, and the ads are not shown in the remainder of the day when the budget is depleted. Arrival times of keyword-search instances, ad positions, ad selections, and sales generated by the ads are random. Therefore, an advertiser faces a dynamic stochastic total net revenue optimization problem subject to a strict budget constraint. Here we formulate and solve this problem using dynamic programming. We show that there is always an optimal dynamic bidding policy. We describe an iterative numerical approximation algorithm that uniformly converges to the optimal solution at an exponential rate of the number of iterations. We illustrate the algorithm on numerical examples. Because dynamic programing calculations of the optimal bidding policies are computationally demanding, we also propose both static and dynamic alternative bidding policies. We numerically compare the performances of optimal and alternative bidding policies by systematically changing each input parameter. The relative percentage total net revenue losses of the alternative bidding policies increases with the budget loading, but were never more than 3.5 % of maximum expected total net revenue. The best alternative to the optimal bidding policy turned out to be a static greedy bidding policy. Finally, statistical estimation of the model parameters is visited.