Chi Seng Pun^{1}

Abstract: This paper studies a class of expected utility maximization problems with respect to a controlled state process with multiple noises, whose pairwise correlations are equal and ambiguous. Using the ...

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9 results found

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01 Sep 2015-

Abstract: The importance of modelling correlation has long been recognised in the field of portfolio management, with largedimensional
multivariate problems increasingly becoming the focus of research. This paper provides a straightforward
and commonsense approach toward investigating a number of models used to generate forecasts of the correlation
matrix for large-dimensional problems.We find evidence in favour of assuming equicorrelation across various portfolio
sizes, particularly during times of crisis. During periods of market calm, however, the suitability of the constant
conditional correlation model cannot be discounted, especially for large portfolios. A portfolio allocation problem is used to compare forecasting methods. The global minimum variance portfolio and Model Confidence Set are used to compare methods, while portfolio weight stability and relative economic value are also considered.

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Topics: Portfolio optimization (71%), Replicating portfolio (68%), Portfolio (65%) ... read more

10 Citations

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Abstract: This paper studies mean-variance portfolio selection problem subject to proportional transaction costs and no-shorting constraint We do not impose any distributional assumptions on the asset returns By adopting dynamic programming, duality theory, and a comparison approach, we manage to derive a semi-closed form solution of the optimal dynamic investment policy with the boundaries of buying, no-transaction, selling, and liquidation regions Numerically, we illustrate the properties of the optimal policy by depicting the corresponding efficient frontiers under different rates of transaction costs and initial wealth allocations We nd that the efficient frontier is distorted due to the transaction cost incurred We also examine how the width of the no-transaction region varies with different transaction cost rates Empirically, we show that our transaction-cost-aware policy outperforms the transaction-cost-unaware policy in a realistic trading environment that incurs transaction costs

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Topics: Transaction cost (57%), Efficient frontier (56%), Portfolio (52%)

4 Citations

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Abstract: This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to fina...

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2 Citations

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Abstract: In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of -- the seminal work of Kramkov & Schachermayer [18]. Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.

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Topics: Duality (mathematics) (56%), Trading strategy (51%)

2 Citations

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Abstract: This paper studies a class of robust mean–variance portfolio selection problems with state-dependent risk aversion. Model uncertainty, in the sense of considering alternative dominated models, is introduced to the problem to reflect the investor’s uncertainty-averse preference. To characterise the robust portfolios, we consider closed-loop equilibrium control and spike variation approaches. Moreover, we show that a closed-loop equilibrium strategy exists and is unique under some technical conditions. This partially addresses open problems left in Bjork et al. (Finance Stoch. 21:331–360, 2017) and Pun (Automatica 94:249–257, 2018). By using a necessary and sufficient condition for the equilibrium, we manage to derive the analytical form of the equilibrium strategy via the unique solution to a nonlinear ordinary differential equation system. To validate the proposed closed-loop control framework, we show that when there is no uncertainty, our equilibrium strategy is reduced to the strategy in Bjork et al. (Math. Finance 24:1–24, 2014), which cannot be deduced under the open-loop control framework.

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Topics: Mathematical finance (53%)

1 Citations

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46 results found

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Abstract: Publisher Summary A common hypothesis about the behavior of limited liability asset prices in perfect markets is the random walk of returns or in its continuous-time form the geometric Brownian motion hypothesis, which implies that asset prices are stationary and log-normally distributed. A number of investigators of the behavior of stock and commodity prices have questioned the accuracy of the hypothesis. In an earlier study described in the chapter, it was examined that the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the “geometric Brownian motion” hypothesis. Under the additional assumption of a constant relative or constant absolute risk-aversion utility function, explicit solutions for the optimal consumption and portfolio rules were derived. The changes in these optimal rules with respect to shifts in various parameters such as expected return, interest rates, and risk were examined by the technique of comparative statics. This chapter presents an extension of these results for more general utility functions, price behavior assumptions, and income generated also from noncapital gains sources. If the geometric Brownian motion hypothesis is accepted, then a general separation or mutual fund theorem can be proved such that, in this model, the classical Tobin mean-variance rules hold without the objectionable assumptions of quadratic utility or of normality of distributions for prices. Hence, when asset prices are generated by a geometric Brownian motion, the two-asset case can be worked on without loss of generality.

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Topics: Geometric Brownian motion (64%), Intertemporal portfolio choice (60%), Mutual fund separation theorem (59%) ... read more

4,736 Citations

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Abstract: Acts are functions from states of nature into finite-support distributions over a set of 'deterministic outcomes'. We characterize preference relations over acts which have a numerical representation by the functional J(f) = min > {∫ uo f dP / P∈C } where f is an act, u is a von Neumann-Morgenstern utility over outcomes, and C is a closed and convex set of finitely additive probability measures on the states of nature. In addition to the usual assumptions on the preference relation as transitivity, completeness, continuity and monotonicity, we assume uncertainty aversion and certainty-independence. The last condition is a new one and is a weakening of the classical independence axiom: It requires that an act f is preferred to an act g if and only if the mixture of f and any constant act h is preferred to the same mixture of g and h. If non-degeneracy of the preference relation is also assumed, the convex set of priors C is uniquely determined. Finally, a concept of independence in case of a non-unique prior is introduced.

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Topics: Preference relation (56%), Convex set (54%), Preference (economics) (53%) ... read more

2,373 Citations

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Abstract: EVER SINCE mathematicians first began to study the measurement of risk there has been general agreement on the following proposition: Expected values are computed by multiplying each possible gain by the number of ways in which it can occur, and then dividing the sum of these products by the total number of possible cases where, in this theory, the consideration of cases which are all of the same probability is insisted upon. If this rule be accepted, what remains to be done within the framework of this theory amounts to the enumeration of all alternatives, their breakdown into equi-probable cases and, finally, their insertion into corresponding classifications…

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Topics: Kelly criterion (52%)

2,245 Citations

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Abstract: EVER SINCE mathematicians first began to study the measurement of risk there has been general agreement on the following proposition: Expected values are computed by multiplying each possible gain by the number of ways in which it can occur, and then dividing the sum of these products by the total number of possible cases where, in this theory, the consideration of cases which are all of the same probability is insisted upon. If this rule be accepted, what remains to be done within the framework of this theory amounts to the enumeration of all alternatives, their breakdown into equi-probable cases and, finally, their insertion into corresponding classifications…

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Topics: Kelly criterion (51%)

1,851 Citations

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Abstract: This presentation comes from the Improving Portfolio Performance With Quantitative Models conference held in New York on April 13, 1989.

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Topics: Portfolio (55%), Presentation (51%)

861 Citations