• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.513-533
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• 2004

We present the pricing and hedging method for options with general payoffs in the presence of transaction costs. The convexity of the payoff function-gamma of the options- is an important issue under transaction costs. When the payoff function is convex, Leland-style pricing and hedging method still works. However, if the payoff function is of general form, additional assumptions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payoff is convex as in Leland 〔11〕 and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. 〔10〕, Avellaneda and Paras 〔1〕. We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payoff into difference of two options each of which has a convex payoff. This method is consistent with a scheme of separating out the seller's and buyer's position of an option. In this paper, we first present a simple linear valuation method of general payoff options, and also propose in the last section more efficient hedging scheme which costs less to hedge options.

• Journal of KIISE:Software and Applications
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• v.27 no.3
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• pp.257-265
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• 2000

There is much selective confliction in nature where selfish and rational individuals exists. Iterated Prisoner's Dilemma (IPD) game deals with this problem, and has been used to study on the evolution of cooperation in social, economic and biological systems. So far, there has been much work about the relationship of the number of players and cooperation, strategy learning as a machine learning and the effect of payoff functions to cooperation. In this paper, We attempt to investigate the cooperative coalition size according to payoff functions, and observe the relationship of localization and the evolution of cooperation in NIPD (N-player IPD) game. Experimental results indicate that cooperative coalition size increases as the gradient of the payoff function for cooperation becomes steeper than that of defector's payoff function, or as the minimum coalition size gets smaller, Moreover, the smaller the neighborhood of interaction is, the higher the cooperative coalition emerges through the evolution of population.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.53 no.11
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• pp.630-635
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• 2004

Generation companies(Genco) submit the supply functions as a bidding function to a bid market in a competitive electricity market. The profits of Gencos vary in accordance with the bid functions, so the selection of a bidding function plays a key role in increasing their profits. In order to get a profitable bidding function which is usually linear, it is required to modify adequately the intersection and the slope of a linear supply function. This paper presents an analysis of the selection of the supply function from the viewpoint of Nash equilibrium(NE). Four types of bidding function parameters are used for analizing the electricity market. The competition of selecting bidding parameters is modeled as two level games in this research. One is a subgame where a certain type of parameters is given and the players compete to select values of the underlying parameters. The other is an overall game where the players compete to select a profitable type among the four types of parameters. The NEs in both games are computed by an using analytic method and a payoff matrix method. It is verified in case studies for the NE of overall game to satisfy the equilibrium condition.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.30 no.2
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• pp.89-98
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• 2007

In this paper the economic value of weather forecasts is valuated for profit-oriented enterprise decision-making situations. Value is estimated in terms of monetary profits (or benefits) resulted from the forecast user's decision under the specific payoff structure, which is represented by a profit/loss ratio model combined with a decision function and a value score (VS). The forecast user determines a business-related decision based on the probabilistic forecast, the user's subjective reliability of the forecasts, and the payoff structure specific to the user's business environment. The VS curve for a meteorological forecast is specified by a function of the various profit/loss ratios, providing the scaled economic value relative to the value of a perfect forecast. The proposed valuation method based on the profit/loss ratio model and the VS is adapted for hypothetical sets of forecasts and verified for site-specific probability of precipitation forecast of 12 hour and 24 hour-lead time, which is generated from Korea meteorological administration (KMA). The application results show that forecast information with shorter lead time can provide the decision-makers with great benefits and there are ranges of profit/loss ratios in which high subjective reliability of the given forecast is preferred.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.10
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• pp.3810-3830
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• 2015

In this paper, we investigate the differential game theoretic approach for distributed dynamic cooperative power control in cognitive radio ad hoc networks (CRANETs). First, a payoff function is defined by taking into consideration the tradeoff between the stock of accumulated power interference to the primary networks and the dynamic regulation of the transmit power of secondary users (SUs). Specifically, the payoff function not only reflects the tradeoff between the requirement for quickly finding the stable available spectrum opportunities and the need for better channel conditions, but also reveals the impact of the differentiated types of data traffic on the demand of transmission quality. Then the dynamic power control problem is modeled as a differential game model. Moreover, we convert the differential game model into a dynamic programming problem to obtain a set of optimal strategies of SUs under the condition of the grand coalition. A distributed dynamic cooperative power control algorithm is developed to dynamically adjust the transmit power of SUs under grand coalition. Finally, numerical results are presented to demonstrate the effectiveness of the proposed algorithm for efficient power control in CRANETs.

• Proceedings of the KIEE Conference
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• summer
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• pp.710-712
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• 2004

Generation companies(Genco) submit the supply functions as a bidding function to a bid market in a competitive electricity market. The profits of Gencos vary in accordance with the bid functions, so the selection of a bidding function plays a key role in increasing their profits. This paper presents an analysis of the selection of the supply function from the viewpoint of Nash equilibrium(NE). Four types of bidding function parameters are used for analizing the electricity market. The competition of selecting bidding parameters is modeled as subgame and overall game in this research. The NEs in both game are computed by using analytic method and payoff matrix method. It is verified in case studies for the NE of overall game to satisfy the equilibrium condition.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.2
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• pp.97-106
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• 2005

This paper presents a method for evaluating the nash equilibrium of the Cournot model for N-Gencos in wholesale electricity market. In wholesale electricity market, the strategies of N-Gencos can be applied to the game model under the conditions, which the Gencos determine their strategies to maximize their benefit. Generally, the Lemke algorithm has known as the approach to evaluate the mixed nash equilibrium in the only two-player game model. In this paper, we have developed the necessary condition for obtaining the mixed nash equilibrium of N-player by using the Lemke algorithms. However, it is difficult to find the mixed nash equilibrium of two more players by using the analytic method since those have the nonlinear characteristics. To overcome the above problem, we have formulated the object function satisfied with the proposed necessary conditions for N-player nash equilibrium and applied the modified particle swarm optimization (PSO) method to obtain the equilibrium for N-player. To present the effectiveness the proposed necessary condition and the evaluation approach, this paper has shown the results of equilibrium of sample system and the cournot game model for 3-players.

• IEMEK Journal of Embedded Systems and Applications
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• v.18 no.4
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• pp.195-201
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• 2023

The degree of contribution each sensor makes towards the total information gathered by all sensors is not uniform in spatially correlated sensor fields. Considering bit allocation problem in such a spatially correlated sensor field, the number of bits to be allocated to each sensor should be proportional to the degree of contribution the sensor makes. In this paper, we deploy Shapley value, a representative solution concept in cooperative game theory, and utilize it in order to quantify the degree of contribution each sensor makes. Shapley value is a system that determines the contribution of an individual player when two or more players work in collaboration with each other. To this end, we cast the bit allocation problem into a cooperative game called bit allocation game where sensors are regarded as the players, and a payoff function is given in the criteria of mutual information. We show that the Shapley value fairly quantifies an individual sensor's contribution to the total payoff achieved by all sensors following its desirable properties. By numerical experiments, we confirm that sensor that needs more bits to cover its area has larger Shapley value in spatially correlated sensor fields.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.383-398
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• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.5
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• pp.848-853
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• 2007

This paper presents a methodology of estimating incomplete information in electricity markets for analyzing the gaming behavior of Generating Companies (GENCOs). Each GENCO needs to model its opponents' unknown information of strategic biddings and cost functions. In electricity markets with complete information, each GENCO knows its rivals' payoff functions and tries to maximize its own profit at Nash equilibriurnl Nli) by acknowledging the rivals' cost function. On the other hand, in the incomplete information markets, each GENCO lacks information about its rivals. Load patterns can change continuously due to many factors such as weather, price, contingency, etc. In this paper, we propose the method of the estimation of the opponents' cost function using market price, transaction quantities. and customer load patterns. A numerical example with two GENCOs is illustrated to show the basic idea and effectiveness of the proposed methodology.