AN ONLINE PORTFOLIO SELECTION ALGORITHM WITH REGRET LOGARITHMIC IN PRICE VARIATION

We present a novel efficient algorithm for portfolio selection which theoretically attains two desirable properties:

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On-Line Portfolio Selection Using Multiplicative Updates

We present an on-line investment algorithm that achieves almost the same wealth as the best constant-rebalanced portfolio determined in hindsight from the actual market outcomes. The algorithm employs a multiplicative update rule derived using a framework introduced by Kivinen and Warmuth. Our algorithm is very simple to implement and requires only constant storage and computing time per stock in each trading period. We tested the performance of our algorithm on real stock data from the New York Stock Exchange accumulated during a 22-year period. On these data, our algorithm clearly outperforms the best single stock as well as Cover's universal portfolio selection algorithm. We also present results for the situation in which the investor has access to additional "side information."     

UNIVERSAL SEMICONSTANT REBALANCED PORTFOLIOS

In this paper, we investigate investment strategies that can rebalance their target portfolio vectors at arbitrary investment periods. These strategies are called semiconstant rebalanced portfolios in Blum and Kalai and Helmbold et al. Unlike a constant rebalanced portfolio, which must rebalance at every investment interval, a semiconstant rebalanced portfolio rebalances its portfolio only on selected instants. Hence, a semiconstant rebalanced portfolio may avoid rebalancing if the transaction costs outweigh the benefits of rebalancing. In a competitive algorithm framework, we compete against all such semiconstant portfolios with an arbitrary number of rebalancings and corresponding rebalancing instants. We investigate this framework with and without transaction costs and demonstrate sequential portfolios that asymptotically achieve the wealth of the best semiconstant rebalanced portfolios whose number of rebalancings and instants of rebalancings are tuned to the individual sequence of price relatives.     

ASYMPTOTICALLY OPTIMAL PORTFOLIOS

This paper extends to continuous time the concept of universal portfolio introduced by Cover (1991). Being a performance weighted average of constant rebalanced portfolios, the universal portfolio outperforms constant rebalanced and buy-and-hold portfolios exponentially over the long run. an asymptotic formula summarizing its long-term performance is reported that supplements the one given by Cover. A criterion in terms of long-term averages of instantaneous stock drifts and covariances is found which determines the particular form of the asymptotic growth. A formula for the expected universal wealth is given.     

Model-free portfolio theory: A rough path approach

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Approximating Large Diversified Portfolios

This paper considers a financial market with asset price dynamics modeled by a system of lognormal stochastic differential equations. A one‐dimensional stochastic differential equation for the approximate evolution of a large diversified portfolio formed by these assets is derived. This identifies the asymptotic dynamics of the portfolio as being a lognormal diffusion. Consequentially an efficient way for computing probabilities, derivative prices, and other quantities for the portfolio are obtained. Additionally, the asymptotic strong and weak orders of convergence with respect to the number of assets in the portfolio are determined.     

MODELING LIQUIDITY EFFECTS IN DISCRETE TIME

We study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox–Ross–Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.     

BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME

This paper formulates and studies a general continuous-time behavioral portfolio selection model under Kahneman and Tversky's (cumulative) prospect theory, featuring S-shaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a behavioral model could be easily mis-formulated (a.k.a. ill-posed) if its different components do not coordinate well with each other. Certain classes of an ill-posed model are identified. A systematic approach, which is fundamentally different from the ones employed for the utility model, is developed to solve a well-posed model, assuming a complete market and general Itô processes for asset prices. The optimal terminal wealth positions, derived in fairly explicit forms, possess surprisingly simple structure reminiscent of a gambling policy betting on a good state of the world while accepting a fixed, known loss in case of a bad one. An example with a two-piece CRRA utility is presented to illustrate the general results obtained, and is solved completely for all admissible parameters. The effect of the behavioral criterion on the risky allocations is finally discussed.     

How Norway’s sovereign wealth fund negative screening affects firms’ value and behaviour

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Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation

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Parametric Portfolio Policies in the Surplus Consumption Ratio

The surplus consumption ratio plays a central role as a state variable in successful attempts to explain the time series properties of stock and bond prices with consumption‐based asset pricing models. In this paper, optimal portfolio policies for a strategic investor who maximizes the conditionally expected utility of terminal wealth are parameterized as a polynomial in the surplus consumption ratio. Optimal portfolio policies are estimated using a method of moments estimator based on Euler equations. Unconditional portfolio policies are rejected in favor of conditional policies. Lower order polynomials are rejected in favor of higher order polynomials. Optimal stock and bond allocations are clearly countercyclical.     

Entrepreneurship: skills and financing

This article analyzes an occupational choice model with risk-averse agents who are heterogeneous in terms of skills and wealth in a setting with financial frictions. We show that high- and middle-wealth individuals endowed with a balanced portfolio of skills upgrade their skills so that the resulting portfolio of skills is more balanced and choose entrepreneurship. In contrast, middle-wealth individuals endowed with an unbalanced portfolio of skills and low-wealth individuals specialize in the skill in which they have an absolute advantage and choose paid employment. Deeper financial development, a more balanced portfolio of skills, lower entrepreneurial risk, and a higher liquidation value for projects result in more entrepreneurship and higher welfare, while wealth redistributions and financial subsidies to entrepreneurs have an ambiguous effect on welfare.     

NO-FREE-LUNCH EQUIVALENCES FOR EXPONENTIAL LÉVY MODELS UNDER CONVEX CONSTRAINTS ON INVESTMENT

We provide equivalence of numerous no-free-lunch type conditions for financial markets where the asset prices are modeled as exponential Lévy processes, under possible convex constraints in the use of investment strategies. The general message is the following: if any kind of free lunch exists in these models it has to be of the most egregious type, generating an increasing wealth. Furthermore, we connect the previous to the existence of the numéraire portfolio , both for its particular expositional clarity in exponential Lévy models and as a first step in obtaining analogues of the no-free-lunch equivalences in general semimartingale models, a task that is taken on in Karatzas and Kardaras (2007) .     

CVaR HEDGING USING QUANTIZATION‐BASED STOCHASTIC APPROXIMATION ALGORITHM

In this paper, we investigate a method based on risk minimization to hedge observable but nontradable source of risk on financial or energy markets. The optimal portfolio strategy is obtained by minimizing dynamically the conditional value‐at‐risk (CVaR) using three main tools: a stochastic approximation algorithm, optimal quantization, and variance reduction techniques (importance sampling and linear control variable), as the quantities of interest are naturally related to rare events. As a first step, we investigate the problem of CVaR regression, which corresponds to a static portfolio strategy where the number of units of each tradable assets is fixed at time 0 and remains unchanged till maturity. We devise a stochastic approximation algorithm and study its a.s. convergence and weak convergence rate. Then, we extend our approach to the dynamic case under the assumption that the process modeling the nontradable source of risk and financial assets prices is Markovian. Finally, we illustrate our approach by considering several portfolios in connection with energy markets.     

Housing wealth effect in emerging economies

In this paper I estimate the impact of changes in real and financial wealth on private consumption for a panel of 17 emerging economies from Asia and Central and Eastern Europe. Households' consumption, income and the two measures of real and financial wealth – proxied by house and stock market prices – are found to be difference-stationary and co-integrated; by means of recent econometric techniques for heterogeneous panels, i.e. the pooled mean group estimator, inference is drawn about the long- and short-run relationships between the variables of interest. The main result of the analysis shows that both real and financial wealth positively affect households' consumption in the long-run, with the elasticity of housing wealth being larger than that of stock market wealth. Moreover, there is also a significant short-run adjustment from income, stock prices and house prices on consumption, i.e. consumption adjusts to its long-run relationship with lags. When the model is run for the two groups of countries separately, the long-run impact of an increase (decrease) in house prices is generally higher in Central and Eastern European economies with respect to Asian ones, which make them more vulnerable to further adverse housing market developments.     

MONOTONICITY PROPERTIES OF OPTIMAL INVESTMENT STRATEGIES FOR LOG-BROWNIAN ASSET PRICES

Consider the geometric Brownian motion market model and an investor who strives to maximize expected utility from terminal wealth. If the investor's relative risk aversion is an increasing function of wealth, the main result in this paper proves that the optimal demand in terms of the total wealth invested in a given risky portfolio at any date is decreasing in absolute value with wealth. The proof depends on the functional form of the Brunn–Minkowski inequality due to Prékopa.     

A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome

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HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12

We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the “wealth process” is a supermartingale. Next, we prove the existence of an optimal solution to the portfolio optimization problem of maximizing utility from terminal wealth in the same model, we also characterize this solution via a transformation to a hedging problem: the optimal portfolio is the one that hedges the inverse of marginal utility evaluated at the shadow state-price density solving the corresponding dual problem, if such exists. We can then use the optimal shadow state-price density for pricing contingent claims in this market. the mathematical tools are those of continuous-time martingales, convex analysis, functional analysis, and duality theory.     

OPTIMAL PORTFOLIO, CONSUMPTION-LEISURE AND RETIREMENT CHOICE PROBLEM WITH CES UTILITY

We study optimal portfolio, consumption-leisure and retirement choice of an infinitely lived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution (CES) function of consumption and leisure. We integrate in one model the optimal consumption-leisure-work choice, the optimal portfolio selection, and the optimal stopping problem in which the agent chooses her retirement time. The economic agent derives utility from both consumption and leisure, and is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. We solve the problem analytically by considering a variational inequality arising from the dual functions of the optimal stopping problem. The optimal retirement time is characterized as the first time when her wealth exceeds a certain critical level. We provide the critical wealth level for retirement and characterize the optimal consumption-leisure and portfolio policies before and after retirement in closed forms. We also derive properties of the optimal policies. In particular, we show that consumption in general jumps around retirement.