Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization

We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it can be expressed as a difference of two functions. The first term is the composition of a convex function with concave arguments and the second term a composition of a convex function with convex arguments. This structure allows us to derive a global lower bound, or minorant, on the CPT utility, which we can use in a minorization-maximization (MM) algorithm for maximizing CPT utility. We further show that the problem is amenable to a simple convex-concave (CC) procedure which iteratively maximizes a local approximation. Both of these methods can handle small and medium size problems, and complex (but convex) portfolio constraints. We also describe a simpler method that scales to larger problems, but handles only simple portfolio constraints

Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY

We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be expressed in an analytical form. In general the problem can be made tractable via dualization, which turns a min-max problem into a min-min problem. Dualization requires expertise and is tedious and error-prone. We demonstrate how CVXPY can be used to automate this dualization procedure in a user-friendly manner. Our framework allows practitioners to specify and solve robust ERM problems with a general class of convex losses, capturing many standard regression and classification problems. Users can easily specify any complex uncertainty set that is representable via disciplined convex programming (DCP) constraints

Strategic Asset Allocation with Illiquid Alternatives

We address the problem of strategic asset allocation (SAA) with portfolios that include illiquid alternative asset classes. The main challenge in portfolio construction with illiquid asset classes is that we do not have direct control over our positions, as we do in liquid asset classes. Instead we can only make commitments; the position builds up over time as capital calls come in, and reduces over time as distributions occur, neither of which the investor has direct control over. The effect on positions of our commitments is subject to a delay, typically of a few years, and is also unknown or stochastic. A further challenge is the requirement that we can meet the capital calls, with very high probability, with our liquid assets. We formulate the illiquid dynamics as a random linear system, and propose a convex optimization based model predictive control (MPC) policy for allocating liquid assets and making new illiquid commitments in each period. Despite the challenges of time delay and uncertainty, we show that this policy attains performance surprisingly close to a fictional setting where we pretend the illiquid asset classes are completely liquid, and we can arbitrarily and immediately adjust our positions. In this paper we focus on the growth problem, with no external liabilities or income, but the method is readily extended to handle this case

Discovery of surrogate agonists for visceral fat Treg cells that modulate metabolic indices in vivo

© Fernandes et al. T regulatory (Treg) cells play vital roles in modulating immunity and tissue homeostasis. Their actions depend on TCR recognition of peptide-MHC molecules; yet the degree of peptide specificity of Treg-cell function, and whether Treg ligands can be used to manipulate Treg cell biology are unknown. Here, we developed an Ab-peptide library that enabled unbiased screening of peptides recognized by a bona fide murine Treg cell clone isolated from the visceral adipose tissue (VAT), and identified surrogate agonist peptides, with differing affinities and signaling potencies. The VAT-Treg cells expanded in vivo by one of the surrogate agonists preserved the typical VAT-Treg transcriptional programs. Immunization with this surrogate, especially when coupled with blockade of TNFα signaling, expanded VAT-Treg cells, resulting in protection from inflammation and improved metabolic indices, including promotion of insulin sensitivity. These studies suggest that antigen-specific targeting of VAT-localized Treg cells could eventually be a strategy for improving metabolic disease