1. Introduction 2. Linear programming: theory and algorithms 3. LP models: asset/liability cash flow matching 4. LP models: asset pricing and arbitrage 5. Nonlinear programming: theory and algorithms 6. NLP volatility estimation 7. Quadratic programming: theory and algorithms 8. QP models: portfolio optimization 9. Conic optimization tools 10. Conic optimization models in finance 11. Integer programming: theory and algorithms 12. IP models: constructing an index fund 13. Dynamic programming methods 14. DP models: option pricing 15. DP models: structuring asset backed securities 16. Stochastic programming: theory and algorithms 17. SP models: value-at-risk 18. SP models: asset/liability management 19. Robust optimization: theory and tools 20. Robust optimization models in finance Appendix A. Convexity Appendix B. Cones Appendix C. A probability primer Appendix D. The revised simplex method Bibliography Index.

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Optimization Methods in Finance

Robust M-estimation of multivariate GARCH models

https://members.femto-st.fr/sites/femto-st.fr.laurent_larger/files/content/Homepage_ll_fichiers/pdf_files/cl_NN14.pdf

Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs.

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Stochastic Nonlinear Time Series Forecasting Using Time-Delay Reservoir Computers: Performance and Universality

This article presents theoretical and empirical methodology for estimation and modeling of multivariate volatility processes It surveys the model specifications and the estimation methods Multivariate GARCH models covered are VEC (initially due to Bollerslev, Engle and Wooldridge, 1988), diagonal VEC (DVEC), BEKK (named after Baba, Engle, Kraft and Kroner, 1995), Constant Conditional Correlation Model (CCC, Bollerslev, 1990), Dynamic Conditional Correlation Model (DCC models of Tse and Tsui, 2002, and Engle, 2002) I illustrate approach by applying it to daily data from the Belgrade stock exchange, I examine two pairs of daily log returns for stocks and index, report the results obtained, and compare them with the restricted version of BEKK, DVEC and CCC representations The methods for estimation parameters used are maximum log-likehood (in BEKK and DVEC models) and twostep approach (in CCC model)

/pdf/modeling-multivariate-volatility-processes-theory-and-u80p6ll1ir.pdf

Modeling Multivariate Volatility Processes: Theory and Evidence

This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our results demonstrate that constrained nonlinear programming is a worthwhile exercise for GARCH models, especially for the bivariate and trivariate cases, as they offer a significant improvement in the quality of the solution of the optimization problem over the diagonal VECH and the BEKK representations of the multivariate GARCH model.

/pdf/constrained-nonlinear-programming-for-volatility-estimation-2vczq04dn8.pdf

Sven Leyffer

Papers

Constrained Nonlinear Programming for Volatility Estimation with GARCH Models