Predictable Forward Performance Processes: The Binomial Case We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose parameters are random and updated dynamically as the market evolves. We show that the key step in the construction of the associated predictable forward performance process is to solve a singleperiod inverse investment problem, namely, to determine, periodbyperiod and conditionally on the current market information, the endtime utility function from a given initialtime value function. We reduce this inverse problem to solving a functional equation and establish conditions for the existence and uniqueness of its solutions in the class of inverse marginal functions.

Portfolio problems with two levels decisionmakers: Optimal portfolio selection with pricing decisions on transaction costs Abstract   This paper presents novel bilevel leaderfollower portfolio selection problems in which the financial intermediary becomes a decisionmaker. This financial intermediary decides on the unit transaction costs for investing in some securities, maximizing its benefits, and the investor chooses his optimal portfolio, minimizing risk and ensuring a given expected return. Hence, transaction costs become decision variables in the portfolio problem, and two levels of decisionmakers are incorporated: the financial intermediary and the investor. These situations give rise to general Nonlinear Programming formulations in both levels of the decision process. We present different bilevel versions of the problem: financial intermediaryleader, investorleader, and social welfare; besides, their properties are analyzed. Moreover, we develop Mixed Integer Linear Programming formulations for some of the proposed problems and effective algorithms for some others. Finally, we report on some computational experiments performed on data taken from the Dow Jones Industrial Average, and analyze and compare the results obtained by the different models.