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We show how to solve Merton optimal investment stochastic control problem for Hawkesbased models in finance and insurance (Propositions 1 and 2), i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t) (risk process) of an insurance company with the amount of claims described by the risk model based on GCHP. The main approach in both cases is to use functional central limit theorem for the GCHP to approximate it with a diffusion process. Then we construct and solve Hamilton-Jacobi-Bellman (HJB) equation for the expected utility function. The novelty of the results consists of the new Hawkes-based models and in the new optimal investment results in finance and insurance for those models.

We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and consumption when compared to the averages among the other agents. We derive a closed form solution for the n-player game and the corresponding mean field game. This solution is unique in the class of equilibria with constant investment and continuous time-dependent consumption, both independent of the wealth of the agent. Compared to the classical Merton problem with one agent, the competitive model exhibits a wide range of highly nonlinear and non-monotone dependence on the agents’ risk tolerance and competitiveness parameters. Counter-intuitively, competitive agents with high risk tolerance may behave like non-competitive agents with low risk tolerance.

Substantial R &D efforts are currently directed towards the development of combined heat and power (CHP) systems that automatically and seamlessly connect to the power grid. In this paper we develop a real options model to assess the impact that the operational flexibility characterizing such systems will have on the optimal timing and capacity associated with investments in CHP plants. We take the viewpoint of a manufacturer operating in an energy-intensive industry who contemplates investing in CHP. We discuss and compare investments in two types of CHP systems: a standard one that is operationally rigid and a technologically advanced one that is operationally flexible. The interaction between temporal and operational flexibility under uncertainty and irreversibility is central to our analysis. We show that operational flexibility guarantees earlier investment but has an ambiguous effect in terms of capacity. In particular, when operational flexibility is very valuable the potential investor is opting for investing in a plant with larger productive capacity. The potential investor chooses a smaller CHP unit if otherwise. A numerical exercise calibrated using data from the Italian pulp and paper and electricity industries complements our theoretical analysis.

Purpose This study aims to test whether over-investment is associated with environmental, social and governance (ESG) variation (i.e. inequality) across its dimensions, which, if so, would imply the prioritization of the interests of some stakeholders over those of others. Design/methodology/approach Drawing on a global sample of 29,428 observations across nine sectors and 41 countries between 2003 and 2019, the authors executed a country-industry-year fixed-effects regression analysis. In the robustness tests, this study also used the entropy balancing and propensity score matching approaches. Findings The authors found that while firm over-investment increases social pillar inequality, it reduces environmental pillar inequality. Further analysis revealed that the over-investment strategy decreases (increases) ESG inequality in low (high) environmental and social performers. This outcome could be of relevance to internal governance mechanisms and policymaking as ESG inequality might raise legitimacy concerns and hamper the long-term sustainability of firms. Practical implications The outcome of the study could be of relevance to internal governance mechanisms as well as policymaking. Considering financial constraints, firms should maintain a balanced strategy between firm investment and addressing stakeholder interests. Otherwise, over-investment might reduce environmental and social engagement in some dimensions, which could prompt criticisms and legitimacy concerns about firms and some stakeholders. Originality/value Past research has intensively focused on whether ESG – rather than ESG inequality – is associated with investment (in)efficiency. In addition, it has mostly formulated the causality running from ESG to firm investment, and hence, the literature lacks heterogeneity in this respect. Nevertheless, the authors believe that the potential effect of firm investment on ESG is of critical importance and has implications for determining whether over-investment causes variations across ESG engagement. Thus, the authors addressed this gap in the literature by investigating the relationship between over-investment and ESG inequality.

Related to a stochastic investment problem which aims to deter-mine when is it better to first invest a larger amount of money and afterwards a smaller one, in this paper we introduce a new preference relation between random variables. We investigate the link between this new relation and some well-known stochastic order relations and present some characterization properties illustrated with numerical examples.

This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and “level II order book data”, i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the order book information makes our study much more realistic, since it is more closely related to the real behavior of many financial markets. Besides, ambiguity may be incorporated, which allows us to overcome the model-risk, since a potential discrepancy between the real (and maybe unknown) probabilities and the estimated ones is taken into account. Though the portfolio choice problem is not at all linear, its dual problem becomes a linear goal programming problem, and, consequently, the absence of duality gap allows us to solve the portfolio choice problem in an easy way. Furthermore, the double dual problem is linear too, and its solution also leads to the Pareto-efficient frontier. Lastly, we explore the influence on the Pareto-efficient frontier of the existence of “golden strategies”, i.e., investment strategies whose tail (or downside) risk is strictly lower than their price. Numerical experiments involving all the findings are implemented in a derivative market where both future contracts and call/put options may be traded.

E-mobility represents an important part of the EU’s green transition and one of the key drivers for reducing CO2 pollution in urban areas. To accelerate the e-mobility sector’s development it is necessary to invest in energy infrastructure and to assure favorable conditions in terms of competitive electricity prices to make the technology even more attractive. Large peak consumption of parking lots which use different variants of uncoordinated charging strategies increases grid problems and increases electricity supply costs. On the other hand, as observed lately in energy markets, different, mostly uncontrollable, factors can drive electricity prices to extreme levels, making the use of electric vehicles very expensive. In order to reduce exposure to these extreme conditions, it is essential to identify the optimal way to supply parking lots in the long term and to apply an adequate charging strategy that can help to reduce costs for end consumers and bring higher profit for parking lot owners. The significant decline in photovoltaic (PV) and battery storage technology costs makes them an ideal complement for the future supply of parking lots if they are used in an optimal manner in coordination with an adequate charging strategy. This paper addresses the optimal power supply investment problem related to parking lot electricity supply coupled with the application of an optimal EV charging strategy. The proposed optimization model determines optimal investment decisions related to grid supply and contracted peak power, PV plant capacity, battery storage capacity, and operation while optimizing EV charging. The model uses realistic data of EV charging patterns (arrival, departure, energy requirements, etc.) which are derived from commercial platforms. The model is applied using the data and prices from the Croatian market.

In this paper we study optimal investment when the investor can peek some time units into the future, but cannot fully take advantage of this knowledge because of quadratic transaction costs. In the Bachelier setting with exponential utility, we give an explicit solution to this control problem with intrinsically infinite-dimensional memory. This is made possible by solving the dual problem where we make use of the theory of Gaussian Volterra integral equations.

To profit from price oscillations, investors frequently use threshold-type strategies where changes in the portfolio position are triggered by some indicators reaching prescribed levels. In this paper we investigate threshold-type strategies in the context of ergodic control. We make the first steps towards their optimization by proving ergodic properties of related functionals. Assuming Markovian price increments satisfying a minorization condition and (one-sided) boundedness we show, in particular, that for given thresholds, the distribution of the gains converges in the long run. We also extend recent results on the stability of overshoots of random walks from the i.i.d. increment case to Markovian increments, under suitable conditions.