We examine the optimal trading strategy of a market maker managing stock inventory under short-term market fluctuations, particularly shifts in trading intensity and volatility. To capture these dynamics, we model market condition changes using Poisson jump processes. Within this framework, we derive analytic solutions for the market maker’s optimal bid and ask quotes and analyze the resulting inventory dynamics. Our findings highlight how transient changes in market activity shape optimal quoting behavior and inventory management.
In cooperative games with coalition and graph structures, the Owen graph value was first introduced and characterized by Vázquez-Brage et al. [Games Econ. Behav. 12 (1996) 42-53]. We provide a new axiomatic characterization of the Owen graph value by employing coalitional marginality principle.
This paper studies the precedence constrained knapsack problem (PCKP) and proposes clique-based cut selection with constraint reduction (CBCS-CR). The method has the following innovations: (i) a novel strategy for selecting clique-based cuts that enables the identification of stronger cuts; (ii) an innovative approach that integrates cuts with constraint reduction by deleting precedence constraints dominated by strengthened clique cuts, thereby controlling model size growth. Computational experiments show that our method outperforms directly solving the original formulation with Gurobi.
We study a bargaining game in which players negotiate the division of a random surplus before its realization, using quantile-based preferences and unanimous consent. Under the assumption that a single player possesses the strictly highest risk threshold, we show that the stationary subgame perfect equilibrium (SSPE) is unique and no-delay: the most risk-tolerant player becomes the residual claimant who absorbs all aggregate uncertainty, while every other player receives a deterministic share proportional to his recognition probability. This mechanism relies on transfers—without them, risk thresholds become irrelevant. When the strict ordering condition is relaxed, multiple SSPEs arise.
This paper develops a data-driven chance-constrained optimization framework with complex-valued decision variables under uncertainty. A Wasserstein ambiguity set centered at the empirical distribution is used to derive worst-case CVaR approximations for individual and joint probabilistic constraints. The individual formulation admits a convex reformulation, whereas the joint formulation leads to a biconvex problem efficiently handled through a convex sequential method. Numerical experiments, including an application to the minimum variance distortionless response, demonstrate the robustness and efficiency of the proposed approach.
Chance constraints are widely used in optimization under uncertainty. This paper aims to show the eventual convexity (EV) of chance constraints with skewed generalized hyperbolic (GH) random variables. We prove that the densities of GH distributions are α-decreasing, and obtain exact convex reformulations for separable jointly chance constraints with GH distributions. We provide numerical results to compute the α-decreasing threshold parameters and show the EV of the feasible set together with the computational tractability to solve the associated optimization problems.
In this paper, we investigate the pricing of American options under a slowly varying stochastic volatility framework, which effectively captures the long-term dynamics of the underlying asset. Employing an asymptotic expansion method, we derive a new analytical approximation for both the option price and the associated optimal exercise boundary. To further enhance computational efficiency, we adopt Kim’s integral equation approach for the leading-order term. In addition, we provide a rigorous error analysis that establishes explicit accuracy guarantees, thereby filling an important gap in the existing literature.
Let Ln be the optimal TSP tour length for n uniform points in [0, 1]2. By the Beardwood–Halton–Hammersley Theorem, Ln/n→β almost surely, with β ≈ 0.71 according to simulation. The best bounds for β are currently 0.6277 ≤ β ≤ 0.90380. We propose a variation of an established upper-bounding strategy, which stitches short segments into a valid TSP tour, and assess its improvement through simulation. We further rigorously improve the upper bound to 0.90367.
We study a single-period newsvendor with an advance order from a low-cost supplier with random lead time and a contingent backup order from a reliable, costlier source placed at time τ < T if needed. The resulting two-stage problem is concave and admits simple critical-fractile/threshold policies driven by conditional delivery probabilities. We characterize when to use only the reliable source, only the unreliable source, or both. We further analyze the effect of the backup-order timing, giving monotonicity conditions and identifying when the initial and backup orders can be non-monotone, with numerical examples for illustration.
We consider a preemptive single-machine scheduling problem with the late work criterion and convex resource-dependent processing times. The objective is to minimize the sum of total late work and resource consumption. While the problem was previously solved in quadratic time, we present a linear-time algorithm, assuming that jobs are ordered by nondecreasing due dates. The result strengthens the usefulness of this problem as a relaxation for the NP-hard non-preemptive counterpart.
We introduce a novel importance sampling method, k-moment tilting (KMT), for estimating tail probabilities of sums of random variables. KMT constructs sampling density by tilting each marginal density with an individual moment parameter. We develop a general procedure yielding closed-form optimal parameters for independent non-identically distributed (i.n.d.) random variables, which is highly effective for heavy-tailed settings. Furthermore, we establish asymptotic optimality for the Pareto distribution and numerically illustrate the consistent efficiency of the KMT method.
This paper studies pricing in a spatial duopoly where consumers choose both outlets and travel routes, generating route and at-location congestion. In a regular regime, the equilibrium conditions admit a reduced representation whose Jacobian has a symmetric rank-one Schur complement structure. This structure gives sufficient conditions for local sign-stable inversion and implies that at-location congestion dampens own-price sensitivity. A markup increase follows under an additional local best-response condition.
The probabilistic branch-and-bound (PBnB) algorithms were proposed for general simulation optimization problems. Like their deterministic counterparts, PBnB will prune a subregion when the estimated probability that it contains good solutions is low. It was anticipated that the PBnB algorithms can guarantee the solution quality with pre-specified probability upon termination. We prove theoretically and numerically that such statistical guarantee of solution is not possessed by PBnB in general, by some specific counterexamples. We also briefly discuss the potential reasons of such failure and some insights from the counterexamples. It remains an open question how to fix the PBnB algorithms or impose sufficient conditions on the simulation optimization problems.
We study fair submodular maximization under a knapsack constraint. Given a ground set E which is partitioned into k disjoint groups G1,…,Gk, a weight function w:E↦R+, a monotone submodular function f:2E↦R+, a budget B and a set of non-negative integers ℓi, ui for i=1,…,k, the goal is to find a set S⊆E with the maximum f(S) subject to ∑e ∈ Swe ≤ B and ℓi ≤ |S ∩ Gi| ≤ ui for every i ∈ [k]. We give the first polynomial-time constant approximation algorithm for an arbitrary number of groups that satisfies the knapsack constraint and all fairness constraints exactly. Its approximation ratio is (1−e−3)/(4−e−3)≈0.241, resolving a previously open problem.
This paper investigates stochastic comparisons of active redundancies for the fault-tolerant fail-safe systems. Sufficient conditions are presented for one, two, and multiple active redundancies for stochastic orders. Finally, some numerical examples and data analysis could illustrate our theoretical findings.
In the k-center problem, we are given a set of points P in a finite N point metric and are tasked with finding a set S⊆P of at most k centers such that the maximum distance of any input point to its closest center is minimized. In the (k, z)-center problem, we are additionally allowed to remove z points from P and are then tasked with minimizing the k-center clustering cost on the remaining points.The k-center problem has been studied in sliding window streams where we are given an infinite stream of points and are asked to solve a problem of interest on the most recent N points of the stream. Here, the state of the art is a 6+ε approximation storing O(kε−1log(Δ)) points [Cohen-Addad, Schwiegelshohn, Sohler, ICALP 2016], where Δ is the aspect ratio. In this paper, we present a sliding window algorithm for the (k, z) problem. Our algorithm stores O((k+z)zε−1log(Δ)) points. If we are willing to use ε−1logΔ·(2(k+z+1)·(z+2)k) running time upon querying a solution, the algorithm achieves a (6+ε) approximation ratio. If we insist upon polynomial time (e.g. O(ε−1logΔ·(k5+z5)z5)), then it still achieves a (8+ε) approximation ratio.
Proof-of-stake protocols lock tokens into staking positions, shrinking the tradable float. We develop a continuous-time model in which price-impact volatility is a convex decreasing function of the float. Two results emerge. Conditional return variance amplifies as the float contracts, with amplification accelerating in high-staking regimes. Protocol changes that shift the long-run staking target produce persistent volatility regime transitions, with convergence speed governed by protocol adjustment capacity. Liquid-staking tokens attenuate both effects, with attenuation increasing in their liquidity parameter.
We propose a new associated game built around the marginal contributions of players to the complementary coalition. We use this associated game in an associated consistency axiom. We identify the subset of efficient, symmetric and linear sharing rules that satisfy this associated consistency and show that, amongst these, only the egalitarian value is monotonic or self-dual.
We study bilevel linear programs that involve only continuous variables at the lower level. Standard solution approaches reformulate these problems as single-level mixed-integer linear programs (MILPs) via complementary slackness or strong duality (SD). The SD-based reformulation, however, requires that all upper-level variables are bounded integers. To overcome this restriction, we approximate the upper-level continuous variables using binary expansions with controlled precision and derive the corresponding SD-based reformulations. The resulting MILPs provide lower and upper bounds for the original bilevel programs.
One of the most famous conjectures in combinatorial optimization is the four-thirds conjecture, which states that the integrality gap of the Subtour LP relaxation of the TSP is equal to 43. For 40 years, the best known upper bound was 1.5, due to Wolsey [1]. Recently, Karlin, Klein, and Oveis Gharan [2] showed that the max entropy algorithm for the TSP gives an improved bound of 1.5−10−36. In this paper, we show that the maximum entropy algorithm is a 107-approximation for half-integral cycle cut instances of the TSP. This class of instances contains examples which demonstrate the subtour LP has an integrality gap of at least 43, as well as examples showing that the performance of the max entropy algorithm is no better than 118. We note that in [3], the authors gave an algorithm upper bounding the integrality gap of this class of instances by 43, so this work does not (and could not) provide an improved bound on the integrality gap. However, since there is no reason to believe that the analysis of the maximum entropy algorithm on general instances is tight, our work provides hope (and potentially direction) for improved analysis on other instance classes.
