Rank-dependent ppredictableforward performance processes

Predictable forward performance processes(PFPPs)are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period ahead.This is a common scenario in which a controlling agent frequently re-calibrates her model.We introduce a new class of PFPPs based on rank-dependent utility,generalizing existing models that are based on expected utility theory(EUT).We establish existence of rank-dependent PFPPs under a conditionally complete market and exogenous probability distortion functions which are updated periodically.We show that their construction reduces to solving an integral equation that generalizes the integral equation obtained under EUT in previous studies.We then propose a new approach for solving the integral equation via theory of Volterra equations.We illustrate our result in the special case of conditionally complete Black-Scholes model.

Mean field and n-player games in Ito-diffusion markets under forward performance criteria

We study n-player games of portfolio choice in general common Ito-diffusion markets under relative performance criteria and time monotone forward utilities.We,also,consider their continuum limit which gives rise to a forward mean field game with unbounded controls in both the drift and volatility terms.Furthermore,we allow for general(time monotone)preferences,thus departing from the homothetic case,the only case so far analyzed.We produce explicit solutions for the optimal policies,the optimal wealth processes and the game values,and also provide representative examples for both the finite and the mean field game.

Predictable forward performance processes in complete markets

We establish existence of Predictable Forward Performance Processes(PFPPs)in conditionally complete markets,which has been previously shown only in the binomial setting.Our market model can be a discrete-time or a continuous-time model,and the investment horizon can be finite or infinite.We show that the main step in construction of PFPPs is solving a one-period problem involving an integral equation,which is the counterpart of the functional equation found in the binomial case.Although this integral equation has been partially studied in the existing literature,we provide a new solution method using the Fourier transform for tempered distributions.We also provide closedform solutions for PFPPs with inverse marginal functions that are completely monotonic and establish uniqueness of PFPPs within this class.We apply our results to two special cases.The first one is the binomial market and is included to relate our work to the existing literature.The second example considers a generalized Black–Scholes model which,to the best of our knowledge,is a new result.

Impact of Heterogeneity on Forwarding Schemes in Opportunistic Networks

In the paper, we concentrate on the infl uence of heterogeneity on the performance of forwarding algorithms under opportunistic networks. Therefore, we first describe two different heterogeneous network models, and capture the heterogeneity which concern mobile nodes' contact dynamics under the individual models and the spatial models. Then we investigate inter-contact time is not fully follow exponential distribution and compare the performance of the delivery delay between direct forwarding protocol and three-hop forwarding protocol under three network models. We illustrate the performance of message delivery delay under the spray and wait protocol and prophet protocol from simulation results. Our simulation results show that the heterogeneity should be considered for the performance of forwarding protocols.

Forward robust portfolio selection: The binomial case

We introduce a new approach for optimal portfolio choice under model ambiguity by incorporating predictable forward preferences in the framework of Angoshtari et al.[2].The investor reassesses and revises the model ambiguity set incrementally in time while,also,updating his risk preferences forward in time.This dynamic alignment of preferences and ambiguity updating results in time-consistent policies and provides a richer,more accurate learning setting.For each investment period,the investor solves a worst-case portfolio optimization over possible market models,which are represented via a Wasserstein neighborhood centered at a binomial distribution.Duality methods from Gao and Kleywegt[10];Blanchet and Murthy[8]are used to solve the optimization problem over a suitable set of measures,yielding an explicit optimal portfolio in the linear case.We analyze the case of linear and quadratic utilities,and provide numerical results.

Optimal investment and consumption with forward preferences and uncertain parameters

We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity.Incompleteness stems from general investment constraints,while model uncertainty is represented by a convex and compact set of plausible model parameter processes.Following the max-min criteria in traditional(backward)robust control,we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes.We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies.Furthermore,we present additional results within the class of homothetic constant relative risk aversion(CRRA)processes.Within this class,we investigate the relationship between forward performance processes on wealth and those on consumption,establishing an interesting dominance through time.