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## Sequential δ-optimal consumption and investment for stochastic volatility markets with unknown parameters

Theory of Probability and Its Applications. 2016. Vol. 60. No. 4. P. 533-560.

Berdjane B., Pergamenschikov S.

We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock price appreciation rate. The volatility parameter is driven by an external economic factor modeled as a diffusion process of Ornstein- Uhlenbeck type with unknown drift. We use the dynamical programming approach and find an optimal financial strategy which depends on the drift parameter. To estimate the drift coefficient we observe the economic factor Y in an interval [0, T0] for fixed T0 > 0, and use sequential estimation. We show that the consumption and investment strategy calculated through this sequential procedure is δ-optimal.

Kelbert M., Moreno-Franco H. A., Working papers by Cornell University. Series cond-mat.soft "arxiv.org" ( 2020

This paper studies a mixed singular/switching stochastic control problem for a multidimensional diffusion with multiple regimes on a bounded domain. Using probabilistic, partial differential equation (PDE) and penalization techniques, we show that the value function associated with this problem agrees with the solution to a Hamilton-Jacobi-Bellman (HJB) equation. In that way, we see that the ...

Added: October 31, 2020

Tsitovich F. I., Tsitovich I. I., , in: 6th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, ICUMT 2014; St. Petersburg; Russian Federation; 6 October 2014 through 8 October 2014. .: IEEE, 2015.. P. 501-506.

We apply the suboptimal sequential nonparametric hypotheses testing approach for effectiveness of a statistical decision by sample space reducing. Numerical examples of the sample space reducing are given when an appropriate reducing makes it possible to construct robust sequential nonparametric hypotheses testing with a smaller mean duration time then one on the total sample space. ...

Added: September 10, 2015

Kurbangaleev M. Z., Информационные системы и математические методы в экономике (электронный научный журнал) 2012 No. 3 P. 121-127

This paper reviews difficulties concerning a development of single-name CDS price (spread) dynamics model for the purpose of determination of margin requirements. It also discusses a possibility to construct such a model using information about respective equity prices and option implied volatilities. Finally, it presents the basic step towards the former idea demonstrating results for ...

Added: July 18, 2012

Lakshina V. V., Silaev A. M., Economics Bulletin 2016 Vol. 36 No. 4 P. 2368-2380

The paper proposes the thorough investigation of in-sample and out-of-sample performance of five GARCH and two stochastic volatility models, estimated on the Russian financial data. The data includes prices of Aeroflot and Gazprom stocks and Ruble against US dollar exchange rates. In our analysis we use probability integral transform for in-sample comparison and Mincer-Zarnowitz regression ...

Added: December 27, 2016

Moreno-Franco H. A., Applied Mathematics and Optimization 2018 Vol. 78 No. 1 P. 25-60

The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton–Jacobi–Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in this work arises in singular stochastic control problems where the state process is a controlled d-dimensional Lévy process. ...

Added: October 12, 2016

Gafarov B., Do unobserved components models forecast inflation in Russia? / Высшая школа экономики. Series EC "Economics". 2013. No. WP BRP 35/EC/2013.

I apply the model with unobserved components and stochastic volatility (UC-SV) to forecast the Russian consumer price index. I extend the model which was previously suggested as a model for inflation forecasting in the USA to take into account a possible difference in model parameters and seasonal factor. Comparison of the out-of-sample forecasting performance of ...

Added: October 4, 2013

Presnova A., Journal of Physics: Conference Series 2019 No. 1163 P. 1-6

The mathematical model describing the dynamics of HIV in the human body is a nonlinear system of differential equations. This model takes into account the effect of drugs on the body. Thus, it is possible to obtain ”optimal” treatment regimens for patients, which cause minimal harm to the body. In the work for constructing suboptimal ...

Added: March 28, 2019

Savchenko A., Information Sciences 2019 Vol. 489 P. 18-36

The paper addresses the issue of insufficient speed of image recognition methods if the number of classes is rather large. We propose the novel algorithm based on sequential three-way decisions and a formal description of granular computing. Each image is associated with principal component scores of the high-dimensional features extracted by deep convolution neural network. ...

Added: March 20, 2019

Tsitovich I. I., , in: Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference. .: M.: RUDN, 2017.. P. 509-522.

We study the problem of parameters estimating if there is a slight deviation between the parametric model
and real distributions. The estimator is based on suboptimal testing of builded by a special way
nonparametric hypotheses. It is proposed a natural for this problem risk function. We found that the risk
function has an exponential decrease to the mean ...

Added: September 12, 2018

Presnova A., Автоматизация. Современные технологии 2018 Т. 72 № 12 С. 563-569

The problem of searching for optimal control of nonlinear systems is indicated. Using the algorithmic method proposed in this paper, suboptimal control of a nonlinear object is constructed. The necessary assumptions are made for using the method of extended linearization. The example demonstrates the work of an algorithmic method for synthesizing suboptimal controls, and compares ...

Added: October 2, 2018

Savchenko A., Belova N. S., Milov V. R., , in: Analysis of Images, Social Networks and Texts. 4th International Conference, AIST 2015, Yekaterinburg, Russia, April 9–11, 2015, Revised Selected Papers. Vol. 542: Series: Communications in Computer and Information Science.: Switzerland: Springer, 2015.. Ch. 2. P. 14-23.

In this paper we explore an application of the pyramid HOG (Histograms of Oriented Gradients) features in image recognition problem with small samples. A sequential analysis is used to improve the performance of hierarchical methods. We propose to process the next, more detailed level of pyramid only if the decision at the current level is ...

Added: December 4, 2015

Savchenko A., Записки научных семинаров ПОМИ РАН 2021 Т. 499 С. 267-283

In this paper fast image recognition techniques based on statistical sequential analysis are discussed. We examine the possibility to sequentially process the principal components and organize a convolutional neural net- work with early exits. Particular attention is paid to sequentially learn multi-task lightweight neural network model to predict several facial at- tributes (age, gender and ...

Added: January 27, 2021

Tsitovich I. I., Tsitovich F. I., International Journal "Information Models and Analyses" 2013 Vol. 2 No. 1 P. 62-69

We study the problem of testing composite hypotheses versus composite alternatives when there is a slight deviation between the model and the real distribution. The used approach, which we called sub-optimal testing, implies an extension of the initial model and a modification of a sequential statistically significant test for the new model. The sub-optimal test ...

Added: July 21, 2013

Savchenko A., , in: Proceedings of International Joint Conference on Neural Networks 2020 (IJCNN 2020). .: Piscataway: IEEE, 2020.. P. 1-8.

In this paper the problem of high computational complexity of deep convolutional nets in image recognition is considered. An existing framework of adaptive neural networks is extended by appending the separate classifier to intermediate layers. The hierarchical representations of the input image are sequentially analyzed. If the first classifier returns rather high confidence score, the ...

Added: October 15, 2020

Lakshina V. V., Fluke of stochastic volatility versus GARCH inevitability or Which model creates better forecasts? / Высшая школа экономики. Series FE "Financial Economics". 2014. No. 37.

The paper proposes the thorough investigation of in-sample and out-of-sample performance of four GARCH and two stochastic volatility models, estimated on the Russian financial data. The data includes prices of Aeroflot and Gazprom stocks and Ruble against US dollar exchange rates. In our analysis we use probability integral transform for in-sample comparison and Mincer-Zarnowitz regression ...

Added: October 2, 2014

Kelbert M., Moreno-Franco H. A., Advances in Applied Probability 2021 Vol. 54 No. 2

This paper studies a mixed singular/switching stochastic control problem for a
multidimensional diusion with multiple regimes on a bounded domain. Using
probabilistic, partial dierential equation (PDE) and penalization techniques,
we show that the value function associated with this problem agrees with the
solution to a Hamilton-Jacobi-Bellman (HJB) equation. In that way, we see
that the regularity of the value function ...

Added: September 26, 2021

Kelbert M., Moreno-Franco H. A., SIAM Journal on Control and Optimization 2019 Vol. 57 No. 3 P. 2185-2213

In this paper, we guarantee the existence and uniqueness (in the almost everywhere
sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient
constraint and a partial integro-di erential operator whose Levy measure has bounded
variation. This type of equation arises in a singular control problem, where the state
process is a multidimensional jump-di usion with jumps of ...

Added: February 13, 2019

Sokolova A., Savchenko A., Optical Memory and Neural Networks (Information Optics) 2020 Vol. 29 No. 1 P. 19-29

The goal of the study is to increase the computation efficiency of the face recognition that uses feature vectors to describe facial images on photos and videos. These high-dimensional feature vectors are nowadays produced by convolutional neural networks. The methods to aggregate the features generated for each video frame are used to process the video ...

Added: October 25, 2019

Savchenko A., , in: Proceedings of the IEEE 12th International Symposium on Applied Computational Intelligence and Informatics (SACI 2018). .: IEEE, 2018.. P. 515-520.

This paper is focused on still-to-video face recog- nition with large number of subjects based on computation of distances between high-dimensional embeddings extracted using deep convolution neural networks. We propose to utilize granular structures and sequentially process granular representations of all frames of the input video. The coarse-grained granules include only low number of the ...

Added: September 17, 2018