Related papers: Convergence of Optimal Expected Utility for a Sequ…
A number of recent results on optimization problems involving submodular functions have made use of the multilinear relaxation of the problem. These results hold typically in the value oracle model, where the objective function is…
We study super-replication of contingent claims in markets with delayed filtration. The first result in this paper reveals that in the Black--Scholes model with constant delay the super-replication price is prohibitively costly and leads to…
Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid.…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that…
Under a generalised estimating equation analysis approach, approximate design theory is used to determine Bayesian D-optimal designs. For two examples, considering simple exchangeable and exponential decay correlation structures, we compare…
Asymptotic rates of convergence of optimal SOR applied to linear systems with consistently ordered 2-cyclic matrices have been extensively studied in the case where the Jacobi eigenvalues are are real and contained in an interval centered…
A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the…
In this research, an optimal algorithm for the Collatz conjecture is presented. Properties such as the convergence of the algorithm and an equation that relates the algorithm to the classical Collatz conjecture are obtained. It is validated…
We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the L\"uck Approximation Theorem…
This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a…
Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived, by applying van der Corput type lemmas, for functions of logarithmatic singularities, which…
We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…
We determine the optimal amount to invest in a Black-Scholes financial market for an individual who consumes at a rate equal to a constant proportion of her wealth and who wishes to minimize the expected time that her wealth spends in…
Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
Data-driven decision making plays an important role even in high stakes settings like medicine and public policy. Learning optimal policies from observed data requires a careful formulation of the utility function whose expected value is…
Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…
We prove that the Sinkhorn algorithm converges at a rate of $O(k^{-1} \log k)$ in $\ell_1$-norm marginal error, in the asymptotically scalable case. This almost closes the gap between the lower bound $\Omega(k^{-1})$ (Qu et al., 2025) and…
In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak…
This paper considers the fundamental convergence time for opportunistic scheduling over time-varying channels. The channel state probabilities are unknown and algorithms must perform some type of estimation and learning while they make…