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Go is an extremely complex strategic board game despite its simple rules. Recently computer Go based on MCTS plays at human-master level and also has defeated top professional players with handicap games in 19×19 Go. Before implementing computer Go, in this paper we show weakness of pure MC algorithm for playing robust Tic-Tac-Toe game and present alternative method to make up the weakness. Furthermore we show how UCB algorithm works for balancing exploration and exploitation in game tree and discuss the need of a hybrid algorithm combined with UCB and strategy based MCTS, for implementing an enhanced computer Go.

Go is an extremely complex strategic board game despite its simple rules and is the great challenging classic game for AI due to its enormous search space. The computer program AlphaGo finally defeated Fan Hui, the European Go champion, without handicaps on a full-sized 19 ×19 board in October 2015. Monte-Carlo Tree Search (MCTS) is a widely-used algorithm for game-tree search in game playing. MCTS based on statistical sampling is a best-first tree search technique to evaluate states; UCT which is a variant of MCTS uses the UCB1 formula as selection policy. In this paper, we evaluate the performance of MCTS and UCT playing against each other in the game of Tic-Tac-Toe. The experimental results show that the first player UCT is slightly superior to the second player MCTS (54.3±1.0%), the first player is always advantageous to the second player regardless of the MCTS and UCT players, and the result of each game should be a tie if both players do their best in Tic-Tac-Toe. Go is an extremely complex strategic board game despite its simple rules and is the great challenging classic game for AI due to its enormous search space. The computer program AlphaGo finally defeated Fan Hui, the European Go champion, without handicaps on a full-sized 19 ×19 board in October 2015. Monte-Carlo Tree Search (MCTS) is a widely-used algorithm for game-tree search in game playing. MCTS based on statistical sampling is a best-first tree search technique to evaluate states; UCT which is a variant of MCTS uses the UCB1 formula as selection policy. In this paper, we evaluate the performance of MCTS and UCT playing against each other in the game of Tic-Tac-Toe. The experimental results show that the first player UCT is slightly superior to the second player MCTS (54.3±1.0%), the first player is always advantageous to the second player regardless of the MCTS and UCT players, and the result of each game should be a tie if both players do their best in Tic-Tac-Toe.

A new Monte Carlo method is presented to compute the prices of barrier options on stocks. The key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers. It is numerically shown that the first hitting time error of the new Monte Carlo method decreases much faster than that of standard Monte Carlo methods.

베이지안 신경망 모형(Bayesian Neural Networks Models)에서 주어진 입력값(input)은 블랙 박스(Black-Box)와 같은 신경망 구조의 각 층(layer)을 거쳐서 출력값(output)으로 계산된다. 새로운 입력 데이터에 대한 예측값은 사후분포(posterior distribution)의 기대값(mean)에 의해 계산된다. 주어진 사전분포(prior distribution)와 학습데이터에 의한 가능도함수(likelihood functions)를 통해 계산되어진 사후분포는 매우 복잡한 구조를 갖게 됨으로서 기대값의 적분계산에 대한 어려움이 발생한다. 이때 확률적 추정에 의한 근사 방법인 몬테칼로 적분을 이용한다. 이러한 방법으로서 Hybrid Monte Carlo 알고리즘은 우수한 결과를 제공하여준다(Neal 1996). 본 논문에서는 Hybrid Monte Carlo 알고리즘과 기존에 많이 사용되고 있는 Gibbs sampling, Metropolis algorithm, 그리고 Slice Sampling등의 몬테칼로 방법들을 비교한다.

Purpose: Based on research data from 24 listed commercial banks in the period 2012-2022, via regression using the Bayesian approach, the study provided evidence of the optimal threshold in capital structure to improve the stability of banks. Design/methodology/approach: Regarding macroeconomic factors, economic growth tends to erode the banking system's stability, while inflation has a vague impact. Furthermore, through the Bayesian approach via the Monte Carlo algorithm, the study has proposed a method to determine the optimal capital structure for each specific bank to cope with risk. Findings: The results show that the deposit-to-asset value of ACB (Asia Commercial Bank) and CTG (Vietnam Joint Stock Commercial Bank for Industry and Trade) has exceeded the optimal threshold. For non-deposit-to-asset, ACB is approximately at the optimal level; for CTG, this ratio is significantly lower than the optimal level; hence, they could increase this ratio to control risks and create more capital to finance their activities. Research limitations/implications: This research result is an essential practical contribution; it could help specific banks determine the appropriate capital structure to maintain operational stability. Research results could reflect the characteristics of the market being studied. Then, we would use this research result as prior information and combine it with data from each specific bank to estimate the posterior probability of the impact of capital on risk, thereby estimating the appropriate capital structure for the bank that needs to be researched. Originality/value: The paper provided evidence of an optimal capital structure that is associated with lower risk in Vietnamese banks. In addition, foreign capital also tends to improve the stability of the banking system, while bank size increases risks.

Calculating minimal cut sets is a typical quantification method used to evaluate the top event probability for a fault tree. If minimal cut sets cannot be calculated or if the accuracy of the quantification result is in doubt, the Monte Carlo method can provide an alternative for fault tree quantification. The Monte Carlo method for fault tree quantification tends to take a long time because it repeats the calculation for a large number of samples. Herein, proposal is made to improve the quantification algorithm of a fault tree with circular logic. We developed a top-down iteration algorithm that combines the characteristics of the top-down approach and the iteration approach, thereby reducing the computation time of the Monte Carlo method.

Simulation-based hull form optimization is a typical HEB (high-dimensional, expensive computationally, black-box) problem. Conventional optimization algorithms easily fall into the "curse of dimensionality" when dealing with HEB problems. A recently proposed Cross-Entropy (CE) optimization algorithm is an advanced stochastic optimization algorithm based on a probability model, which has the potential to deal with high-dimensional optimization problems. Currently, the CE algorithm is still in the theoretical research stage and rarely applied to actual engineering optimization. One reason is that the Monte Carlo (MC) method is used to estimate the high-dimensional integrals in parameter update, leading to a large sample size. This paper proposes an improved CE algorithm based on quasi-Monte Carlo (QMC) estimation using high-dimensional truncated Sobol subsequence, referred to as the QMC-CE algorithm. The optimization performance of the proposed algorithm is better than that of the original CE algorithm. With a set of identical control parameters, the tests on six standard test functions and a hull form optimization problem show that the proposed algorithm not only has faster convergence but can also apply to complex simulation optimization problems.

본 연구는 Feller제곱근 확률변동성모형에 대한 새로운 베이지언 추론 알고리듬, 알고리듬의 성과에 대한 모의실험 결과, 그리고 알고리듬을 이용한 실증분석 결과를 제시한다. 본 연구의 알고리듬은 수익률과 조건부분산의 결합확률밀도함수로부터 유도되는 조건부분산의 GIG분포 확률커널을 정규분포로 근사하는 방법을 이용하므로 도약과정이나 두꺼운 꼬리를 가지는 수익률분포를 포함하는 확장모형에도 쉽게 적용될 수 있다. 또한 본 연구의 알고리듬과 파티클필터를 통해 얻은 PIT를 이용하는 확률변동성모형 진단 통계량들의 사이즈와 검정력을 비교하는 모의실험 결과를 제시한다. 파라미터 추정에 따른 불확실성에 영향을 받지 않는 대표적인 비모수 검정인 Hong and Li (2005) 검정과 일반화된 잔차의 정규성을 이용하는 고전적 진단통계량들의 사이즈와 검정력에 대한 모의실험 결과, 고전적 진단통계량들의 사이즈왜곡이 심각하지 않을 수 있으며 검정력 또한 Hong-Li옴니버스검정보다 좋을 수 있는 것으로 나타났다.

We develop a new Bayesian Markov Chain Monte Carlo algorithm for Euler-discretized Feller square-root stochastic volatility models and demonstrate the performance of our algorithm through simulations and empirical analyses. Specifically, our algorithm use the Laplace approximation of the posterior density of conditional variance, which is the probability kernel of the generalized inverse gaussian distribution, derived from the joint density of return and conditional variance so that it can be easily applied to the extended stochastic volatility models with such as fat-tailed distributions or Levy jump processes. In addition, we conduct the simulation experiment investigating and comparing the size and power of the parametric specification tests checking certain finite-dimensional moment conditions without correction for parameter estimation uncertainty with that of the nonparametric Hong and Li (2005)’s omnibus test which is not affected by parameter estimation uncertainty. The parametric and nonparametric tests are based on the probability integral transform of the prediction densities of returns obtained using auxiliary particle filter algorithms. Our experiment result shows that the classical parametric specification test may have no worse size distortion and better power than Hong and Li (2005)’s test.

최근에 계산금융 분야에서 복잡한 수식을 이용한 연산이 증가하고 있다. 그리고 계산금융 분야에서 몬테카를로 시뮬레이션은 대표적인 계산방법 중에 하나이다. 그러나 몬테카를로 시뮬레이션은 많은 반복연산을 수행하므로 연산시간이 오래 걸리는 문제점이 있다. 이러한 문제점을 해결하기 위하여 본 논문에서는 몬테카를로 시뮬레이션과 스프레드시트를 병렬로 처리하였다. 또한 실험을 통하여 병렬 스프레드시트의 계산 노드가 증가함에 따라 파생상품의 계산 시간이 단축되는 것을 보였다.

본 논문에서는 환경의 변화에 민감한 시계열 데이터인 주가의 변동과정을 보다 효과적으로 설명하기 위한 방안의 하나로 강화 학습 모형의 도입을 제안하며, 특정 시점의 주가 추세를 평가하는 기준으로 가치도 함수를 채택한다. 가치도 함수의 계산에는 강화 학습 알고리즘의 일종인 Monte Carlo 알고리즘을 적용하고, 신경망 구현에 의해 구한 근사 가치도의 적절성을 평가하였다. 실험 결과로 볼 때, 여타 강화 학습 알고리즘을 추가적으로 적용할 경우, 주가 변동의 시계열적 특성을 더욱 잘 반영할 수 있을 것으로 판단된다.

본 논문은 지수를 추종하기 위해 유전 알고리즘에 몬테카를로 샘플링을 추가한 방법을 제안한다. 몬테카를로 샘플링을 통해 효율적으로 축소된 탐색공간을 탐험하는 유전 알고리즘은 최적의 종목들을 선택한다. 제안된 방법을 KOSPI200 지수 추종에 대하여 실험하였다. 제안된 방법이 몬테카를로 샘플링을 사용하지 않는 유전 알고리즘에 비해 지수 추종 오차가 더 낮고 더 빠르게 수렴하는 것을 보여주었다.

본 논문에서는 선도이자율 모형과 리보이자율 모형 사이의 관계를 이용하여 채권 옵션의 해석적인 해(Analytic Solution; AS)와 몬테 카르로 시뮬레이션(Monte Carlo Simulation; MCS)을 이용한 가격 결정을 다룬다. AS를 이용한 채권 옵션가격 결정은 Ritchken and Sankarasubramanian (RS)의 제한 조건을 이용하여 할인된 채권 가격을 구하는 공식을 유도하고, 선도이자율과 리보이자율 모형의 변동함수 사이의 관계를 활용한다. MCS을 이용한 채권 옵션 가격 결정은 MCS을 이용하여 제시된 조건으로부터 여러 가지 예정된 전개의 시뮬레이션을 활용한다. AS와 MCS을 이용한 가격 결정 방법을 실행하여 얻은 가격을 비교하면 AS와 MCS의 상대오차(Relative Error; RE)를 구할 수 있다. 이때 본 연구의 결과로부터 RE가 약 3.9%가 됨을 확인할 수 있다. 이것은 AS뿐만 아니라 MCS을 이용해도 채권 옵션의 가격을 매우 정확하게 예측할 수 있음을 의미한다.

In this paper, we deal with two pricing of bond options using the relationship between the forward rate model and the Libor rate model. First, we derive a formula for obtaining discounted bond prices using the restrictive condition of the Ritchken and Sankarasubramanian (RS), and then use the volatility function relationship of the forward rate and the Libor rate models to find the analytic solution (AS) of bond options pricing. Second, the price of the bond options is calculated by simulating several scenarios from the presented condition using Monte Carlo Simulation (MCS). Comparing the results of the implementation of the above two pricing methods, the relative error (RE) is obtained, which means the ratio of AS and MCS. From the results, we can confirm that the RE is around 3.9%, which means that the price of the bond options can be predicted very accurately using the MCS as well as AS.

몬테카를로 트리탐색은 최대우선탐색 알고리즘이며, 많은 게임 특히 바둑 게임에 성공적으로 적용되어 왔다. 삼목 게임에서 MCTS 간의 대국을 통해 성능을 평가하고자 했다. 첫 번째 대국자는 항상 두 번째 대국자에 비해 압도적인 우위를 보였으며, 최선의 게임 결과가 무승부가 됨에도 불구하고 첫 번째 대국자가 두 번째 대국자에 비해 우월한 이유를 찾고자 했다. MCTS는 반복적인 무작위 샘플링을 기반으로 하는 통계적 알고리즘이기 때문에, 특히 두 번째 대국자를 위해 전략을 요하는 시급한 문제를 적절히 대처하지 못한다. 이를 위해 전략적 MCTS(S-MCTS)를 제안하며, S-MCTS는 결코 삼목 게임에서 지지 않는다는 것을 보였다.

Monte-Carlo Tree Search(MCTS) is a best-first tree search algorithm and has been successfully applied to various games, especially to the game of Go. We evaluate the performance of MCTS playing against each other in the game of Tic-Tac-Toe. It reveals that the first player always has an overwhelming advantage to the second player; and we try to find out the reason why the first player is superior to the second player in spite of the fact that the best game result should be a draw. Since MCTS is a statistical algorithm based on the repeated random sampling, it cannot adequately tackle an urgent problem that needs a strategy, especially for the second player. For this, we propose a strategic MCTS(S-MCTS) and show that the S-MCTS player never loses a Tic-Tac-Toe game.

각종 선거를 앞두고 여러 여론조사 기관들은 다양한 방법으로 선거 결과를 예측한다. 조사를 통한 선거 예측을 수행하는 데 있어서 발생할 수 있는 문제점 중 하나는 무응답이며 무응답 대체 방법에 따라 예측 결과는 완전히 다른 결과를 생산해 낼 수 있다. 본 연구에서는 무응답 대체의 방법으로 모형을 기반으로 한 대체 방법에 대하여 연구하였다. 특히, 최대 우도 추정 방법을 적용했을 때 무시할 수 없는 무응답 (non-ignorable non-response) 체계 하에서 발생할 수 있는 변방 값 문제를 해결하기 위해 Wei와 Tanner (1990)가 제안한 Monte Carlo EM 알고리즘을 적용하였다. 모의 실험을 통하여 MCEM 방법과 기존의 최대 우도 추정 방법, 베이지안 추정 방법 사이의 비교 연구를 진행하였고 그 결과 MCEM 방법이 기존 방법들에 대한 대안 방법으로 이용될 수 있음을 보였다. 또한 2012년에 시행된 제18대 대통령 선거 당일의 출구조사 자료를 적용하여 실증 분석을 수행하였다. 예측 결과를 비교하기 위해 Bautista 등 (2007)이 제안한 MWPE (modified within precinct error)를 이용하였다.

In predicting an outcome of election using a variety of methods ahead of the election, non-response is one of the major issues. Therefore, to address the non-response issue, a variety of methods of non-response imputation may be employed, but the result of forecasting tend to vary according to methods. In this study, in order to improve electoral forecasts, we studied a model based method of non-response imputation attempting to apply the Monte Carlo Expectation Maximization (MCEM) algorithm, introduced by Wei and Tanner (1990). The MCEM algorithm using maximum likelihood estimates (MLEs) is applied to solve the boundary solution problem under the non-ignorable non-response mechanism. We performed the simulation studies to compare estimation performance among MCEM, maximum likelihood estimation, and Bayesian estimation method. The results of simulation studies showed that MCEM method can be a reasonable candidate for non-response model estimation. We also applied MCEM method to the Korean presidential election exit poll data of 2012 and investigated prediction performance using modified within precinct error (MWPE) criterion (Bautista et al., 2007).