Comprehensive Studies on Financial Asset Management and Asset Pricing under Assumptions of Price Processes with Random Jumps

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Under the assumption that the prices of financial assets and/or values of financial variables follow some diffusion type stochastic processes with random jumps, we have been tried to execute comprehensive studies on financial asset management and arbitrage pricing/replication/hedging of various financial derivatives (derivative assets and contracts) from the various viewpoints of modeling and formalization, theoretical analysis, algorithmic and numerical methods, and so on, and we have obtained a lot of new fruitful results.