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"Model permainan non-kooperatif satu periode dikonstruksi untuk menetapkan premi yang kompetitif di pasar asuransi umum. Pada skripsi ini, konstruksi model permainan nonkooperatif satu periode dengan multiple pemain melibatkan empat komponen penting, yaitu lapse model, loss model, fungsi objektif, dan fungsi kendala solvabilitas. Di bawah perilaku rasional, setiap pemain memilih strategi premi yang akan menghasilkan memaksimalkan keuntungan yang diharapkan dari polis periode selanjutnya. Strategi yang dipilih juga harus memperhatikan aturan solvabilitas yang ditetapkan oleh regulator. Premi yang kompetitif didapatkan dengan mencari solusi dari model permainan, yaitu Nash equilibrium. Nash equilibrium didapatkan dengan mencari solusi dari kondisi Karush-Kuhn-Tucker yang diperluas dan direformulasi menggunakan fungsi komplementaritas. Premi Nash equilibrium selanjutnya digunakan dalam perhitungan probabilitas lapse pemegang polis dan banyaknya pemegang polis periode selanjutnya. Hasil perhitungan tersebut dianalisis dan diinterpretasikan untuk melihat kecenderungan perilaku pemegang polis terhadap premi Nash equilibrium, hubungan premi Nash equilibrium dan pemegang polis baru, serta hubungan premi Nash equilibrium dan tingkat biaya. Berdasarkan parameter referensi untuk asuransi mobil di Jerman tahun 2020, untuk model permainan dengan empat pemain didapatkan bahwa pada tingkat premi Nash equilibrium, pemegang polis cenderung tetap pada perusahaan asuransinya saat ini dan tidak berpindah ke perusahaan asuransi mobil dengan premi yang lebih murah secepat yang diantisipasi oleh model ekonomi. Perusahaan asuransi mobil dengan premi Nash equilibrium terendah mendapatkan pemegang polis baru terbanyak, dan berlaku sebaliknya. Premi Nash equilibrium dan tingkat biaya memiliki hubungan yang searah.

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The one-period non-cooperative game model is constructed to set competitive premiums in the general insurance market. In this thesis, the construction of a one-period noncooperative game model with multiple players involves four important components, namely the lapse model, the loss model, the objective function, and the solvency constraint function. Under rational behavior, each player chooses a premium strategy that will maximize the expected profit from the policy for the next period. The strategy chosen must also pay attention to the solvency rules set by the regulator. A competitive premium is obtained by finding a solution from the game model, namely the Nash equilibrium. Nash equilibrium is obtained by finding the solution of the Karush-Kuhn-Tucker condition which is extended and reformulated using the complementarity function. The Nash equilibrium is then used in calculating the probability lapse and the number of policyholders for the next period. The results of these calculations are analyzed and interpreted to see the behavioral tendencies of policyholders towards the Nash equilibrium premium, the relationship between the Nash equilibrium and new policyholders, as well as the relationship between the Nash equilibrium and the expense rate. Based on the reference parameters for car insurance in Germany in 2020, for a fourplayer game model, it is found that at the Nash equilibrium, policyholders tend to stay with their current insurance companies and do not switch to car insurance companies with lower premiums as quickly as anticipated by economic model. The car insurance company with the lowest Nash equilibrium premium gets the most new policyholders, and vice versa. The Nash equilibrium premium and the expense rate have a unidirectional relationship."

""It has long been recognized that the fundamental theoretical analysis of a market economy is embodied in the Arrow-Debreu-Walras mathematical general equilibrium model, with one great deficiency: the analysis cannot accommodate money and financial institutions. In this groundbreaking book, Ross M. Starr addresses this problem directly, by expanding the Arrow-Debreu model to include a multiplicity of trading opportunities, with the resultant endogenous derivation of money as the carrier of value among them. This fundamental breakthrough is achieved while maintaining the Walrasian general equilibrium price-theoretic structure, augmented primarily by the introduction of separate bid and ask prices reflecting transaction costs. The result is foundations of monetary theory consistent with and derived from modern price theory." -- Back cover."

"Mathematical Optimization and Economic Theory provides a self-contained introduction to and survey of mathematical programming and control techniques and their applications to static and dynamic problems in economics, respectively. It is distinctive in showing the unity of the various approaches to solving problems of constrained optimization that all stem back directly or indirectly to the method of Lagrange multipliers. In the 30 years since its initial publication, there have been many more applications of these mathematical techniques in economics, as well as some advances in the mathematics of programming and control. Nevertheless, the basic techniques remain the same today as when the book was originally published. Thus, it continues to be useful not only to its original audience of advanced undergraduate and graduate students in economics, but also to mathematicians and other researchers who are interested in learning about the applications of the mathematics of optimization to economics.The book is distinctive in that it covers in some depth both static programming problems and dynamic control problems of optimization and the techniques of their solution. It also clearly presents many applications of these techniques to economics, and it shows why optimization is important for economics. Many cchallenging problems for both students and researchers are included."