ALGORITHMIC TRADING OF CO-INTEGRATED ASSETS

2016 ◽  
Vol 19 (06) ◽  
pp. 1650038 ◽  
Author(s):  
ÁLVARO CARTEA ◽  
SEBASTIAN JAIMUNGAL
Keyword(s):  
Closed Form ◽  
Expected Utility ◽  
Asset Prices ◽  
Optimal Solution ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Algorithmic Trading ◽  
Common Component ◽  
Optimal Investment Strategy

We assume that the drift in the returns of asset prices consists of an idiosyncratic component and a common component given by a co-integration factor. We analyze the optimal investment strategy for an agent who maximizes expected utility of wealth by dynamically trading in these assets. The optimal solution is constructed explicitly in closed-form and is shown to be affine in the co-integration factor. We calibrate the model to three assets traded on the Nasdaq exchange (Google, Facebook, and Amazon) and employ simulations to showcase the strategy’s performance.

scholarly journals MAX–MIN OPTIMIZATION PROBLEM FOR VARIABLE ANNUITIES PRICING

2015 ◽  
Vol 18 (08) ◽  
pp. 1550053 ◽  
Author(s):  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ETIENNE CHEVALIER ◽  
IDRIS KHARROUBI ◽  
THOMAS LIM
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Worst Case ◽  
Variable Annuities ◽  
Minimization Problems ◽  
Optimal Investment Strategy ◽  
Utility Indifference

In this paper, we study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts, namely guaranteed minimum death benefits and guaranteed minimum living benefits that allow the insured to withdraw money from the associated account. Here, the price of variable annuities corresponds to a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine the indifference fee rate. We focus on the worst case for the insurer, assuming that the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawal strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensitivity.

scholarly journals Optimal investment strategies in a CIR framework

2000 ◽  
Vol 37 (4) ◽  
pp. 936-946 ◽  
Author(s):  
Griselda Deelstra ◽  
Martino Grasselli ◽  
Pierre-François Koehl
Keyword(s):  
Financial Markets ◽  
Interest Rates ◽  
Utility Function ◽  
Closed Form ◽  
Continuous Time ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Optimal Investment Strategy ◽  
Optimal Investment Problem

We study an optimal investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. Closed form formulae for the optimal investment strategy are obtained by assuming the completeness of financial markets and the CRRA utility function. In particular, we study the behaviour of the solution when time approaches the terminal date.

scholarly journals Optimal investment strategies in a CIR framework

2000 ◽  
Vol 37 (04) ◽  
pp. 936-946 ◽  
Author(s):  
Griselda Deelstra ◽  
Martino Grasselli ◽  
Pierre-François Koehl
Keyword(s):  
Financial Markets ◽  
Interest Rates ◽  
Utility Function ◽  
Closed Form ◽  
Continuous Time ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Optimal Investment Strategy ◽  
Optimal Investment Problem

We study an optimal investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. Closed form formulae for the optimal investment strategy are obtained by assuming the completeness of financial markets and the CRRA utility function. In particular, we study the behaviour of the solution when time approaches the terminal date.

scholarly journals Mathetical problem of banking assets diversification

2021 ◽  
pp. 85-88
Author(s):  
V. R. Kulian ◽  
O. O. Yunkova
Keyword(s):  
Mathematical Formulation ◽  
Optimal Solution ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Point Of View ◽  
Investment Risk ◽  
Expected Return ◽  
Optimal Investment Strategy ◽  
Optimal Values ◽  
Distribution Vector

In article we consider a problem of optimal investment strategy by a commercial bank building. This task is actual and the development of a procedure to solve it can help in making investment banking decisions. The general formulation of the problem consists of two criteria. The first one is to maximize the expected return, and the second is to minimize the risk of the investment transaction. Mathematical formulation of the problem is considered as a problem of nonlinear programming under constraints. The procedure for solving such a two-criteria optimization problem allows to obtain many solutions, which requires further steps to make a single optimal solution. According to the algorithm proposed in the work, the problem is divided into two separate problems of single-criteria optimization. Each of these tasks allows to obtain the optimal values of the investment vector both in terms of its expected return and in terms of investment risk. Additional constraints in the mathematical formulation of the problem, make it possible to take into account factors that, from the point of view of the investor, may influence decision-making. The procedures presented in this work allow to obtain analytical representations of formulas that describe the optimal values of the investment distribution vector for both mathematical formulations of the problem.

scholarly journals Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Regime Switching ◽  
Stock Price ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Power Utility ◽  
Optimal Investment Strategy ◽  
Admissible Strategies ◽  
Definition Of ◽  
Markovian Regime Switching ◽  
Optimal Investment And Consumption

This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

scholarly journals Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1610
Author(s):  
Katia Colaneri ◽  
Alessandra Cretarola ◽  
Benedetta Salterini
Keyword(s):  
Stock Prices ◽  
Regime Switching ◽  
Common Factor ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Insurance Company ◽  
Optimal Investment Strategy

In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

2012 ◽  
Vol 13 (2) ◽  
pp. 228-240 ◽  
Author(s):  
G. Bamberg ◽  
A. Neuhierl
Keyword(s):  
Heavy Tails ◽  
Geometric Mean ◽  
Asymptotic Optimality ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Optimal Investment Strategy ◽  
Optimality Properties ◽  
Heavy Tailed ◽  
The Impact

Abstract The strategy to maximize the long-term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two-asset economy with one risky asset and a risk-free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy-tailed log returns than for light-tailed log returns.

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