Dynamic Programming via Measurable Selection

The aim of this paper is to provide the proof of a Dynamic Programming Principle for a certain class of stochastic control problems with exit time. To this end, a Measurable Selection Theorem is also proved

Exhaustion of resources: a marked temporal process framework

This paper deals with the exhaustion of a replenishable resource, one of the main topics in environmental research. To examine this problem, we construct a mechanism to estimate the probability of depletion under a very small set of assumptions. The stock of the resource is assumed to evolve accordingly to a marked temporal process generated by the shocks occurring in the environment. Our setting is eminently theoretical, and constitutes an effective extension of some important models of stochastic growth regarding sustainability and ruin analysis. Furthermore, the validity of the model is supported through the evidence relative to the paradigmatic cases of water resource planning and oil reserves

Optimal consumption/investment problem with light stocks: A mixed continuous-discrete time approach

This paper addresses the optimal consumption/investment problem in a mixed discrete/continuous time model in presence of rarely traded stocks. Stochastic control theory with state variable driven by a jump-diffusion, via dynamic programming, is used. The theoretical study is validated through numerical experiments, and the proposed model is compared with the classical Merton’s portfolio. Some financial insights are provided

Light Stocks and Wealth Allocation

The aim of this paper is to deal with the problem of wealth allocation. We assume that an investor can share her/his money between consumption, riskless bonds, risky assets frequently traded in the market and illiquid stocks. The financial nature of thin stocks requires the description of their dynamics via jump processes, rather than continuous processes. Therefore, a stochastic control problem in a jump diffusion context is developed. In this paper the dynamic programming approach is adopted, and the optimal investment strategies are derived in closed form

Tax revenues, fiscal corruption and “shame” costs

In this paper we explore tax revenues in a regime of widespread fiscal corruption in a static framework. We prove that the relationship between the tax rate and tax revenues depends on the relevance of the “shame effect” of being detected in a corrupt transaction. In countries with a “low shame” effect, tax revenues grow as the tax rate increases. Moreover, there is a critical tax rate where the growth rate of tax revenues begins to reduce. In countries with a high “shame effect” tax revenues increase up to a threshold value and then decrease

Corruption, evasion and environmental policy: a game theory approach

This paper deals with the interaction between polluting firms, tax inspectors and politicians in a corrupted context. We construct a theoretical game model with incomplete information to discuss the effects of such interaction on environmental policy. In this respect, we believe that the State may pursue environmental protection by employing two alternative strategies: on the one hand, the State can, through greater incentive for the tax inspector, increase the monitoring level that reduces the evasion and thus increase tax revenues (incentive channel); on the other hand, the State can, through greater environmental expenses, increase the compliance of the polluting firm which means lower evasion and, thus greater tax revenues (compliance channel). Clearly, more environmental expenses mean, ceteris paribus, less public resources for the tax inspector's incentive, and vice versa. In this context, we demonstrate that, for a country with a high (low) level of incentives, the incentive (compliance) channel is more efficient than the compliance (incentive) channel. This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Management Mathematics following peer review. The version of record Corruption, evasion and environmental policy: a game theory approach is available online at: https://doi.org/10.1093/imaman/dpu01

Economic growth, corruption and tax evasion

In this paper, we explore tax revenues in a regime of widespread corruption in a growth model. We develop a Ramsey model of economic growth with a rival but non-excludable public good which is financed by taxes which can be evaded via corrupt tax inspectors. We prove that the relationship between the tax rate and tax collection, in a dynamic framework, is not unique, but is different depending on the relevance of the “shame effect”. We show that in all three cases — “low, middle and high shame” countries, the growth rate increases as the tax rate increases up to a threshold value, after which the growth rate begins to decrease as the tax rate increases. But, for intermediate tax rates, the rate of growth for “low shame” countries is lower than that of “uniform shame” countries which is, in turn, lower than that of “high shame” countries. This happens because the growth rate is more sensitive to variations of t in an honest country rather than in a corrupt country

Mean–Variance portfolio selection in presence of infrequently traded stocks

This paper deals with a mean-variance optimal portfolio selection problem in presence of risky assets characterized by low frequency of trading and, therefore, low liquidity. To model the dynamics of illiquid assets, we introduce pure-jump processes. This leads to the development of a portfolio selection model in a mixed discrete/continuous time setting. In this paper, we pursue the twofold scope of analyzing and comparing either long-term investment strategies as well as short-term trading rules. The theoretical model is analyzed by applying extensive Monte Carlo experiments, in order to provide useful insights from a Önancial perspectiv

Roots and effects of financial misperception in a stochastic dominance framework

This work deals with the issue of investors’ irrational behavior and financial products’ misperception. The theoretical analysis of the mechanisms driving erroneous assessment of investment performances is explored. The study is supported by the application of Monte Carlo simulations to the remarkable case of structured financial products. Some motivations explaining the popularity of these complex financial instruments among retail investors are also provided. In particular, investors are assumed to compare the performances of different projects through stochastic dominance rules. Unreasonably and in contrast with results obtained by the application of the selected criteria, investors prefer complex securities to standard ones. In this paper, introducing a new definition for stochastic dominance which presents asymmetric property, we provide theoretical and numerical results showing how investors distort stochastic returns and make questionable investment choices. Results are explained in terms of framing and representative effects, which are behavioral finance type arguments showing how decisions may depend on the way the available alternatives are presented to investors. This is a post-peer-review, pre-copyedit version of an article published in Quality and Quantity. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11135-012-9726-

Firms clustering in presence of technological renewal processes

This paper aims at exploring companies' profit maximization in presence of a hierarchical organization among firms and when technological renewal processes take place. The introduction of a hierarchical structure among rms allows us to describe the reality of the industrial districts. In this respect, some policies for the management of the renewal process in the district are derived