The paper explores local-correlation models for pricing complex financial contracts.
problem Calibrating synthetic quanto forward contracts and composite options.
method Design on-line calibration procedures for local and stochastic volatility models.
result Calibration performance of local-correlation models compared to simpler approximations.
Paper provides a method to price electricity storage contracts using COS technique.
problem Valuation of electricity storage contracts considering physical and operational constraints.
method Uses Fourier-based COS method to price contracts based on stochastic polynomial process.
result The COS method accurately and efficiently prices electricity storage contracts.
Study variance-reduced method for estimating fixed points in Banach spaces.
problem Estimating fixed points of contractive operators in Banach spaces with noisy evaluations.
method Variance-reduced stochastic approximation scheme in Banach spaces.
result Establish non-asymptotic bounds for operator defect and estimation error.
AMM finds optimal contract for LPs to maximize order flow.
problem Maximizing order flow in AMMs with LPs.
method Leader-follower stochastic game, closed-form equilibrium solutions.
result LPs incentivized to add liquidity when external price attracts more noise trading.
Two methods for pricing swing contracts using neural networks or explicit functions.
problem Evaluating optimal energy purchases in swing contracts with firm constraints.
method Two approaches: explicit parametric function and neural network approximation.
result Neural network approach provides better prices in shorter computation time.
Two-layer model studies reinsurance contracts and competition between insurer and reinsurers.
problem Modeling and analyzing reinsurance contracts and competition between insurer and reinsurers.
method Two-layer stochastic game model with insurer negotiating with reinsurers, and reinsurers competing for business.
result Existence and uniqueness of equilibrium strategies for the insurer and reinsurers, characterized in semiclosed form.
Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circul…
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with …
This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.
problem Optimally controlling the evolution of a system's state density over time.
method Analyzes and improves the convergence rates of dynamic Schrödinger systems via geometric and control-theoretic interpretations.
result New insights into improving computation of worst-case contraction coefficients by preconditioning.
Unified framework for solving fixed-point equations in deterministic and stochastic settings.
problem Solving fixed-point equations for seminorm-contractive operators in both deterministic and stochastic contexts.
method Fixed-point theorem and stochastic approximation analysis.
result Unified finite-sample bounds for various reinforcement learning algorithms.
Study pricing options on forward contracts using infinite-dimensional affine models.
problem Pricing European-style options on forward contracts in complex stochastic volatility models.
method Model forward price curves using stochastic partial differential equations modulated by stochastic volatility processes. Analyze two classes of affine stochastic volatility models: Gaussian and pure-jump. Derive conditions for existence of exponential moments and develop semi-closed pricing formulas.
result Developed semi-closed Fourier-based pricing formulas for vanilla call and put options in infinite-dimensional affine models.
Study on convex ordering in stochastic control for swing contracts, proving value function convexity.
problem Pricing of swing contracts under stochastic dynamics.
method Discrete-time stochastic optimal control problem, convexity propagation, Brownian diffusion model, Stein's formula.
result Value function is convex in underlying asset price, relaxation of convexity assumption for semi-convexity.
The paper develops a valuation framework for GLWB-LTC contracts with Levy dynamics and stochastic interest rates.
problem Valuation of GLWB-LTC contracts with financial guarantees, longevity protection, and health-contingent LTC payments.
method Coupling a recombining Hull-White trinomial tree with an IMEX finite difference scheme, incorporating a seven-state health model.
result Hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks.
New bounds for SA with arbitrary norm contractions and Markovian noise.
problem Finite-time analysis of two-time-scale stochastic approximation with arbitrary norm contractions and Markovian noise.
method Use of generalized Moreau envelope for arbitrary norm contractions and solutions of Poisson equation for Markovian noise.
result Mean square error decays at rates of O(1/n2/3) and O(1/n) under different conditions. Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic a…
Model prices commodity futures and index options.
problem Deriving accurate prices for derivative contracts on commodity futures and indices.
method Stochastic local volatility model for commodity futures.
result Model accurately recovers prices of derivative claims.
In this paper, we construct a solution to the optimal contract problem for delegated portfolio management of the fist-best (risk-sharing) type. The novelty of our result is (i) in the robustness of the optimal contract with respect to perturbations of the wealth process (interpreted as capital injections), and (ii) in …
Agent optimizes perpetual contract liquidation with transaction costs and risk.
problem Optimizing perpetual contract liquidation with transaction costs and risk.
method Solving stochastic control problem for optimal trading strategy.
result Closed-form expression and approximations for optimal strategy.
The present work studies and analyzes general defaultable OTC contract in presence of a contingent CSA, which is a theoretical counterparty risk mitigation mechanism of switching type that allows the counterparty of a general OTC contract to switch from zero to full/perfect collateralization and switch back whenever sh…
The paper uses neural networks to price complex life insurance contracts with multiple risk factors.
problem Pricing equity-linked life insurance contracts with various stochastic risk factors.
method Assuming hedging to reduce local variance, the price is expressed as a system of non-linear PDEs. Reformulated as a backward SDE with jumps, solved numerically using neural networks.
result Neural networks provide an efficient numerical solution for pricing these complex contracts.
We develop a pricing rule for life insurance under stochastic mortality in an incomplete market by assuming that the insurance company requires compensation for its risk in the form of a pre-specified instantaneous Sharpe ratio. Our valuation formula satisfies a number of desirable properties, many of which it shares w…
New method improves sampling efficiency in complex stochastic systems.
problem Sampling efficiency in nonconvex stochastic gradient cases.
method Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo.
result Quantitative Gaussian concentration bounds and convergence rates established.
The study examines how alternative resource adequacy contract designs affect market participants' risk profiles and resource mix.
problem The tension between promoting reliability and competition in liberalized electricity markets.
method Constructs a stochastic equilibrium model of a competitive market with incomplete risk trading and computes investment equilibria under different contracting regimes.
result Alternative contracting regimes can induce different risk profiles and resource mixes, affecting market outcomes.
The paper defines fair profit sharing ratios in Islamic PL contracts.
problem Determining fair profit sharing ratios in Islamic PL contracts.
method Introduces c-fair profit sharing ratios and uses econometrics models to compute or approximate them. result Elucidates the relation between profit sharing ratios and economic factors.
Study analyzes fees linked to VIX index in annuity contracts.
problem Impact of VIX-linked fees on annuity contract surrender strategies.
method Two-layer continuous-time Markov chain approximation for fund value process.
result Optimal surrender strategy is more robust to VIX-linked fees.
New MKABSDEs help calculate initial margins in financial contracts.
problem Calculating initial margins in financial contracts with dependencies.
method Introduced MKABSDEs, provided existence and uniqueness, applied to CVaR, used deterministic and Monte-Carlo methods for numerical approximations.
result MKABSDEs provide a new way to solve for initial margins in financial contracts.
A contraction analysis improves model-based RL's error recovery.
problem Theoretical understanding of model-based reinforcement learning.
method Contraction analysis applied to both stochastic and deterministic state transitions.
result Error reduction in cumulative reward using branched rollouts.
The article reviews how to set stochastic volatility model parameters.
problem Choosing parameters for stochastic volatility models.
method Examines existing literature on various methods.
result Different approaches to setting stochastic volatility parameters.
Stochastic differential equation approximation for linear TD(0) under Markovian noise
problem Temporal-difference learning with linear function approximation
method Stochastic differential equation approximation
result Explains the constant-stepsize error floor
New algorithms improve Bayesian linear regression with spike-and-slab priors.
problem Efficiently sampling from Bayesian linear regression models with sparsity-inducing priors.
method Design of two sampling algorithms: Gibbs sampling and Stochastic Localization.
result Stochastic Localization sampler shows significant advantage for poorly designed data matrices.
The paper prices and replicates various financial contracts on a risky asset with stochastic volatility and jumps.
problem Pricing and replicating financial contracts on assets with stochastic volatility and jumps.
method Develops pricing and hedging formulas for various financial contracts, independent of the volatility process dynamics.
result Pricing and hedging formulas for financial contracts are derived without dependence on the volatility process dynamics.
In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the exist…
Study on stochastic hypergradient computation for machine learning problems.
problem Efficient computation of hypergradients in machine learning models.
method Stochastic approximation schemes for hypergradient computation, focusing on empirical risk minimization.
result Bounds for the mean square error of hypergradient approximation under contraction assumptions.
We investigate the framework of privacy amplification by iteration, recently proposed by Feldman et al., from an information-theoretic lens. We demonstrate that differential privacy guarantees of iterative mappings can be determined by a direct application of contraction coefficients derived from strong data processing…
Improved security of smart contracts by classifying them into four categories.
problem Detecting and classifying vulnerabilities in smart contracts efficiently.
method Used AWD-LSTM for multi-class classification, addressing class imbalance.
result Achieved a weighted average Fbeta score of 90.0%.
We introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping factors to their volatility coefficients. The pricing of single underlying Europea…
Unified analysis of stochastic iterative algorithms using Lyapunov functions.
problem Analyzing convergence of stochastic iterative algorithms for fixed-point equations.
method Lyapunov-based techniques for finite-time analysis of stochastic approximation algorithms.
result Unified mean-square convergence guarantees for various algorithms.
Paper develops a model to assess capital requirement for demographic risk using stochastic methods.
problem Quantifying capital requirement for demographic risk in life insurance contracts.
method Stochastic model extending local GAAP to Solvency II framework, proving market consistency.
result Model highlights main drivers of capital requirement evaluation, comparing to GAAP.
One of the peculiarities of power and gas markets is the delivery mechanism of forward contracts. The seller of a futures contract commits to deliver, say, power, over a certain period, while the classical forward is a financial agreement settled on a maturity date. Our purpose is to design a Heath-Jarrow-Morton framew…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract's maturity the contract is perfectly hedged. We derive both the optimal hol…
Study on nonsmooth contractive SA with constant stepsize and Q-learning.
problem Understanding convergence and bias in nonsmooth contractive SA with different noise types.
method Proposed prelimit coupling technique for steady-state convergence and derived asymptotic bias.
result Asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize.
A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the contract plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal(dynamic) withdrawal strategy of a policyh…
We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are applicable to simple objective functions arising in machine learning.
Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.
problem Approximating fixed-points of nonexpansive and contractive operators in normed finite-dimensional spaces.
method Stochastic Halpern iteration with minibatch, analyzing oracle complexity.
result Improved oracle complexity for nonexpansive operators, with a lower bound of Ω(ε−3). A new method improves communication efficiency in distributed learning.
problem Reducing communication overhead in distributed machine learning.
method Transforming contractive compressors into induced unbiased compressors.
result Significant improvements in memory requirements and communication complexity.
In the paper [Probab. Theory Relat. Fields, 100 (1994) 417-428] Xue-Mei Li has shown that the moment stability of an SDE is closely connected with the topology of the underlying manifold. In particular, she gave sufficient condition on SDE on a manifold M under which the fundamental group π1M=0. We prove that in …
CCDF reduces diffusion sampling steps for inverse problems.
problem Slow sampling from diffusion models in inverse problems.
method Starting from a single forward diffusion step with better initialization, followed by stochastic contraction.
result Significantly reduced sampling steps for state-of-the-art reconstruction.