In this paper, we study the problem of optimal investment and proportional reinsurance coverage in the presence of inside information. To be more precise, we consider two firms: an insurer and a reinsurer who are both allowed to invest their surplus in a Black-Scholes-type financial market. The insurer faces a claims process that is modeled by a Brownian motion with drift and has the possibility to reduce the risk involved with this process by purchasing proportional reinsurance coverage. Moreover, the insurer has some extra information at her disposal concerning the future realizations of her claims process, available from the beginning of the trading interval and hidden from the reinsurer, thus introducing in this way inside information aspects to our model. The optimal investment and proportional reinsurance decision for both firms is determined by the solution of suitable expected utility maximization problems, taking into account explicitly their different information sets. The solution of these problems also determines the reinsurance premia via a partial equilibrium approach. Promislow and Young [3], Schmidli [4][5][6], Liang [7], Xu, Wang et al. [8], and references therein. The majority of these works, to the best of our knowledge, deal with the problems of maximization of the expected terminal wealth, or the minimization of the ruin probability of an insurance firm, by choosing the proper investment and/or reinsurance strategies. Also, certain papers have looked at the problem from the point of view of the reinsurer as well, see, for example, Borch [9]. These papers lead to interesting theoretical and mathematical results that may also act as benchmarks for practitioners when trying to decide for choosing the right investment and/or reinsurance policy.However, in the relative literature so far, the assumption that both investors (insurer and reinsurer) operate under the same information set is made. This may be realistic in terms of the information concerning the Black-Scholes financial market, in which both firms may invest, but it is not such an obvious assumption concerning the claims process they are willing to share by entering a reinsurance contract. This paper makes a first attempt in relaxing this assumption by letting one of the firms (the insurer) have some inside information, which is not available at the reinsurer's disposal, concerning her claims process. Then, both firms choose their investment and reinsurance policies in such a way so that the corresponding expected utility function of their terminal wealth is maximized, taking explicitly into account the effect of asymmetric information. The two optimization problems are connected via a partial equilibrium assumption, that is that the insurance market should clear. This natural assumption allows us to determine the equilibrium reinsurance premia, as well as the optimal investment-reinsurance policies of the two firms.The problem of inside information has been treated in the past using the enlargement of filtrations technique that has been...

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The present paper aims to study a robust-entropic optimal control problem arising in the management of financial institutions. More precisely, we consider an economic agent who manages the portfolio of a financial firm. The manager has the possibility to invest part of the firm's wealth in a classical Black-Scholes type financial market, and also, as the firm is exposed to a stochastic cash flow of liabilities, to proportionally transfer part of its liabilities to a third party as a means of reducing risk. However, model uncertainty aspects are introduced as the manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing robust control and dynamic programming techniques, we provide closed form solutions for the cases of the (i) logarithmic; (ii) exponential and (iii) power utility functions. Moreover, we provide a detailed study of the limiting behavior, of the associated stochastic differential game at hand, which, in a special case, leads to break down of the solution of the resulting Hamilton-Jacobi-Bellman-Isaacs equation. Finally, we present a detailed numerical study that elucidates the effect of robustness on the optimal decisions of both players.

In this paper, we study a robust-entropic optimal control problem in the presence of inside information. To be more precise, we consider an economic agent who is allowed to invest her wealth in a classical Black-Scholes type financial market. From the beginning of the trading interval, the agent exclusively possesses some inside information concerning the future realization of the stock price process. However, we assume that she is uncertain as to the validity of this information, thus introducing in this way robust aspects to our model. The aim of the economic agent is to solve an expected utility maximization problem under the worst-case scenario, taking into account her enlarged information set. By formulating this problem as a two-player, zero sum stochastic differential game, we are able to provide closed form solutions for the optimal robust strategies and the robust value function, in the case of the exponential and the power utility functions.