Randomized time‐varying knapsack problems via binary beetle antennae search algorithm: Emphasis on applications in portfolio insurance

Abstract

The knapsack problem is a problem in combinatorial optimization, and in many such problems, exhaustive search is not tractable. In this paper, we describe and analyze the randomized time-varying knapsack problem (RTVKP) as a time-varying integer linear programming (TV-ILP) problem. In this way, we present the on-line solution to the RTVKP combinatorial optimization problem and highlight the restrictions of static methods. In addition, the RTVKP is applied in the field of finance and converted into a portfolio insurance problem. Our methodology is confirmed by simulation tests in real-world data sets, in order to explain being an excellent alternative to traditional approaches.

Binary Beetle Antennae Search Algorithm for Tangency Portfolio Diversification

“…BAS is a meta-heuristic optimization algorithm that mimics the searching behavior of a beetle to find the optimal solution to the problem [24]. A binary version of BAS, called BBAS, introduced in [8]. Because BBAS is only applicable to unconstrained optimization, some supplementary processes must be employed to hold solutions within the feasible range.…”

“…In this way, this approach assists BBAS to manipulate convex or nonconvex constraints more accurately. The BBAS algorithm's principle, however, is similar to that defined in [8].…”

“…Note that the tangency portfolio, also known as the market portfolio, is the most efficient portfolio and arises from the intercept point of the Capital Market Line and the efficient frontier. Because such NLP problems are widely approached by heuristic, a binary beetle antennae search algorithm (BBAS), which is introduced in [8], is employed to provide a solution to the BTPSCC problem. Generally, the beetle antennae search is a memetic meta-heuristic optimization algorithm and has been employed broadly in various scientific fields in the last few years (see [9][10][11][12][13][14][15][16][17]).…”

Diversification of Time-Varying Tangency Portfolio under Nonlinear Constraints through Semi-Integer Beetle Antennae Search Algorithm

“…SIBAS is a hybrid algorithm that combines the beetle antennae search (BAS) algorithm from [10] with the binary BAS (BBAS) algorithm from [11]. Broadly, nature inspired optimization algorithms have been widely used in a variety of scientific domains in recent years, such as finance, computer science and engineering.…”

Unfairly Defiled: A Long Term Perspective on Portfolio Insurance as a Strategy for Limiting Portfolio Losses

“…The method provided downside protection against a long equity position by synthetically replicating a long put option using equity futures, during an era when exchange-traded equity options were not sufficiently liquid [2]. Remarkably, the strategy continues to be an area of interest in financial innovation in modern finance [3][4][5][6][7].…”