Split Bregman iteration for multi-period mean variance portfolio optimization

This paper investigates the problem of defining an optimal long-term investment strategy, where the investor can exit the investment before maturity without severe loss. Our setting is a multi-period one, where the aim is to make a plan for allocating all of wealth among the n assets within a time horizon of m periods. In addition, the investor can rebalance the portfolio at the beginning of each period. We develop a model in Markowitz context, based on a fused lasso approach. According to it, both wealth and its variation across periods are penalized using the l1 norm, so to produce sparse portfolios, with limited number of transactions. The model leads to a non-smooth constrained optimization problem, where the inequality constraints are aimed to guarantee at least a minimum level of expected wealth at each date. We solve it by using split Bregman method, that has proved to be efficient in the solution of this type of problems. Due to the additive structure of the objective function, the alternating split Bregman at each iteration yields to easier subproblems to be solved, which either admit closed form solutions or can be solved very quickly. Numerical results on data sets generated using real-world price values show the effectiveness of the proposed model

L1-regularization for multi-period portfolio selection

In this work we present a model for the solution of the multi-period portfolio selection problem. The model is based on a time consistent dynamic risk measure. We apply l1-regularization to stabilize the solution process and to obtain sparse solutions, which allow one to reduce holding costs. The core problem is a nonsmooth optimization one, with equality constraints. We present an iterative procedure based on a modified Bregman iteration, that adaptively sets the value of the regularization parameter in order to produce solutions with desired financial properties. We validate the approach showing results of tests performed on real data

l1-Regularization in Portfolio Selection with Machine Learning

In this work, we investigate the application of Deep Learning in Portfolio selection in a Markowitz mean-variance framework. We refer to a l1 regularized multi-period model; the choice of the l1 norm aims at producing sparse solutions. A crucial issue is the choice of the regularization parameter, which must realize a trade-off between fidelity to data and regularization. We propose an algorithm based on neural networks for the automatic selection of the regularization parameter. Once the neural network training is completed, an estimate of the regularization parameter can be computed via forward propagation. Numerical experiments and comparisons performed on real data validate the approach

Atrasentan and renal events in patients with type 2 diabetes and chronic kidney disease (SONAR): a double-blind, randomised, placebo-controlled trial

Background: Short-term treatment for people with type 2 diabetes using a low dose of the selective endothelin A receptor antagonist atrasentan reduces albuminuria without causing significant sodium retention. We report the long-term effects of treatment with atrasentan on major renal outcomes. Methods: We did this double-blind, randomised, placebo-controlled trial at 689 sites in 41 countries. We enrolled adults aged 18–85 years with type 2 diabetes, estimated glomerular filtration rate (eGFR)25–75 mL/min per 1·73 m 2 of body surface area, and a urine albumin-to-creatinine ratio (UACR)of 300–5000 mg/g who had received maximum labelled or tolerated renin–angiotensin system inhibition for at least 4 weeks. Participants were given atrasentan 0·75 mg orally daily during an enrichment period before random group assignment. Those with a UACR decrease of at least 30% with no substantial fluid retention during the enrichment period (responders)were included in the double-blind treatment period. Responders were randomly assigned to receive either atrasentan 0·75 mg orally daily or placebo. All patients and investigators were masked to treatment assignment. The primary endpoint was a composite of doubling of serum creatinine (sustained for ≥30 days)or end-stage kidney disease (eGFR <15 mL/min per 1·73 m 2 sustained for ≥90 days, chronic dialysis for ≥90 days, kidney transplantation, or death from kidney failure)in the intention-to-treat population of all responders. Safety was assessed in all patients who received at least one dose of their assigned study treatment. The study is registered with ClinicalTrials.gov, number NCT01858532. Findings: Between May 17, 2013, and July 13, 2017, 11 087 patients were screened; 5117 entered the enrichment period, and 4711 completed the enrichment period. Of these, 2648 patients were responders and were randomly assigned to the atrasentan group (n=1325)or placebo group (n=1323). Median follow-up was 2·2 years (IQR 1·4–2·9). 79 (6·0%)of 1325 patients in the atrasentan group and 105 (7·9%)of 1323 in the placebo group had a primary composite renal endpoint event (hazard ratio [HR]0·65 [95% CI 0·49–0·88]; p=0·0047). Fluid retention and anaemia adverse events, which have been previously attributed to endothelin receptor antagonists, were more frequent in the atrasentan group than in the placebo group. Hospital admission for heart failure occurred in 47 (3·5%)of 1325 patients in the atrasentan group and 34 (2·6%)of 1323 patients in the placebo group (HR 1·33 [95% CI 0·85–2·07]; p=0·208). 58 (4·4%)patients in the atrasentan group and 52 (3·9%)in the placebo group died (HR 1·09 [95% CI 0·75–1·59]; p=0·65). Interpretation: Atrasentan reduced the risk of renal events in patients with diabetes and chronic kidney disease who were selected to optimise efficacy and safety. These data support a potential role for selective endothelin receptor antagonists in protecting renal function in patients with type 2 diabetes at high risk of developing end-stage kidney disease. Funding: AbbVie

A parallel wavelet-based pricing procedure for Asian options

In this paper, we present a parallel pricing algorithm for Asian options based on the Discrete Wavelet Transform. The computational kernel of the pricing model is the solution of integral equations. We obtain a sparse and accurate representation of the kernel of such equations in wavelet function bases. It is worth pointing out that the execution time of our procedure is almost constant with respect to the number of monitoring dates. Thus, our pricing procedure is particularly competitive when the number of monitoring dates is large. We moreover discuss the parallelization of the algorithm. Numerical results that show the accuracy and efficiency of the procedure are reported in the paper

Wavelet Techniques for Option Pricing on Advanced Architectures

This work focuses on the development of a parallel pricing algorithm for Asian options based on a Discrete Wavelet Transform. The pricing process requires the solution of a set of independent Fredholm integral equations of the second kind. Within this evaluation framework, our aim is to develop a robust parallel pricing algorithm based on wavelet techniques for the pricing problem of discrete monitoring arithmetic Asian options. In particular, the Discrete Wavelet Transform is applied in order to approximate the kernels of the integral equations. We discuss both the accuracy of the method and its scalability properties

Fused Lasso approach in portfolio selection

In this work we present a new model based on a fused Lasso approach for the multi-period portfolio selection problem in a Markowitz framework. In a multi-period setting, the investment period is partitioned into sub-periods, delimited by the rebalancing dates at which decisions are taken. The model leads to a constrained optimization problem. Two l1 penalty terms are introduced into the objective function to reduce the costs of the investment strategy. The former is applied to portfolio weights, encouraging sparse solutions. The latter is a penalization on the difference of wealth allocated across the assets between rebalancing dates, thus it preserves the pattern of active positions with the effect of limiting the number of transactions. We solve the problem by means of the Split Bregman iteration. We show results of numerical tests performed on real data to validate our model

Fused Lasso approach in portfolio selection

n this work we present a new model based on a fused Lasso approach for the multi-period portfolio selection problem in a Markowitz framework. In a multi-period setting, the investment period is partitioned into sub-periods, delimited by the rebalancing dates at which decisions are taken. The model leads to a constrained optimization problem. Two l1 penalty terms are introduced into the objective function to reduce the costs of the investment strategy. The former is applied to portfolio weights, encouraging sparse solutions. The latter is a penalization on the difference of wealth allocated across the assets between rebalancing dates, thus it preserves the pattern of active positions with the effect of limiting the number of transactions. We solve the problem by means of the Split Bregman iteration. We showr esults of numerical tests performed on real data to validate our model

Default Risk in a Parallel ALM Software for Life Insurance Portfolios

In this paper we investigate the computational issues in the use of a stochastic model - the doubly stochastic intensity default model - to measure default risk in the development of "internal models", according to the new rules of the Solvency II project. We refer to the valuation framework used in DISAR, an asset-liability management system for the monitoring of portfolios of "Italian style" profit sharing life insurance policies with minimum guarantees. The computational complexity of the overall valuation process requires both efficient numerical algorithms and high performance computing methodologies and resources. Then, to improve the performance, we apply to DISAR a parallelisation strategy based on the distribution of Monte Carlo simulations among the processors of a last generation blade server