Результаты поиска по 'variance':
Найдено статей: 12
  1. Tomonin Y.D., Tominin V.D., Borodich E.D., Kovalev D.A., Dvurechensky P.E., Gasnikov A.V., Chukanov S.V.
    On Accelerated Methods for Saddle-Point Problems with Composite Structure
    Computer Research and Modeling, 2023, v. 15, no. 2, pp. 433-467

    We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and dual variables. First, we consider such problems with smooth composite terms, one of which has finite-sum structure. For this setting we propose a variance reduction algorithm with complexity estimates superior to the existing bounds in the literature. Second, we consider finite-sum saddle-point problems with composite terms and propose several algorithms depending on the properties of the composite terms. When the composite terms are smooth we obtain better complexity bounds than the ones in the literature, including the bounds of a recently proposed nearly-optimal algorithms which do not consider the composite structure of the problem. If the composite terms are prox-friendly, we propose a variance reduction algorithm that, on the one hand, is accelerated compared to existing variance reduction algorithms and, on the other hand, provides in the composite setting similar complexity bounds to the nearly-optimal algorithm which is designed for noncomposite setting. Besides, our algorithms allow one to separate the complexity bounds, i. e. estimate, for each part of the objective separately, the number of oracle calls that is sufficient to achieve a given accuracy. This is important since different parts can have different arithmetic complexity of the oracle, and it is desired to call expensive oracles less often than cheap oracles. The key thing to all these results is our general framework for saddle-point problems, which may be of independent interest. This framework, in turn is based on our proposed Accelerated Meta-Algorithm for composite optimization with probabilistic inexact oracles and probabilistic inexactness in the proximal mapping, which may be of independent interest as well.

    Keywords: saddle-point problem, minimax optimization, composite optimization, accelerated algorithms.
  2. Nikulin V.N., Odintsova A.S.
    Statistically fair price for the European call options according to the discreet mean/variance model
    Computer Research and Modeling, 2014, v. 6, no. 5, pp. 861-874

    We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance hedging risk of the portfolio on the date of maturity of the call option we find a fraction of the asset per unit call option. As a direct consequence we derive the statistically fair lookback call option price in explicit form. In contrast to the famous Black–Scholes theory, any portfolio cannot be regarded as  risk-free because no additional transactions are supposed to be conducted over the life of the contract, but the sequence of independent portfolios will reduce risk to zero asymptotically. This property is illustrated in the experimental section using a dataset of daily stock prices of 37 leading US-based companies for the period from April 2006 to January 2013.

    Keywords: European call options, «mean–variance» model, time-series analysis.
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