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Abstrak :
Penelitian ini dilakukan untuk melihat tingkat efisiensi dari pasar saham di Indonesia dan apakah kondisi pasar mengikuti Efficient Market Hypothesis (EMH) atau Adaptive Market Hypothesis untuk tahun 2000-2019. Dalam penelitian ini, dilakukan pengujian random walk dan martingale untuk menentukan apakah terdapat bukti dari EMH. Hasil penelitian menunjukkan bahwa pasar saham Indonesia bersifat inefisien berdasarkan EMH dan terdapat perubahan dalam tingkat dan periode efisiensi serta inefisiensi pasar. Sebagai analisis lebih lanjut, dilakukan pengujian rolling variance ratio untuk menentukan apakah AMH dapat menjelaskan kondisi pasar saham dengan lebih baik. Berdasarkan hasil yang didapat, periode inefisiensi pasar terjadi pada periode yang sama dengan terjadinya peristiwa besar pada tingkat global dan domestik. Dari keseluruhan hasil analisis, pasar saham Indonesia lebih konsisten dengan AMH. ......This paper examines the degree of market efficiency in Indonesian Stock Exchange and whether it follows either the Efficient Market Hypothesis (EMH) or the Adaptive Market Hypothesis (AMH) for the year 2000-2019. In this study, the approach of random walk hypothesis and martingale were tested to determine if EMH is evident. The result of this study shows that the Indonesian stock market is inefficient based on EMH, but rather having successive periods of efficiency and inefficiency. For further analysis, a rolling variance ratio test approach was applied to find if AMH can provide a better understanding of the stock market. Based on the results, the periods of market inefficiency also coincide with major events that occur on both global and domestic level. Of the overall analysis, results are more consistent with AMH.

Abstrak :
Tugas akhir ini mengkaji harga opsi put Eropa dengan aset dasar zero-coupon bond dan tingkat bunga diasumsikan mengikuti model Vasicek dengan jump. Kajian dilakukan dengan mengkonstruksi kembali persamaan harga opsi put Eropa tersebut. Ukuran jump didefinisikan mengikuti distribusi mixed-exponential. Dengan memanfaatkan infinitesimal generator dan konsep martingale dapat dikonstruksi transformasi Laplace dari distribusi model Vasicek dengan jump. Kemudian, dengan menggunakan hasil transformasi Laplace dari distribusi model Vasicek dengan jump dan konsep equivalent martingale measure dapat dikonstruksi persamaan harga opsi put Eropa dengan aset dasar zero-coupon bond. ......This undergraduate thesis examines the price of European put options with underlying asset zero-coupon bond and the interest rate following the Vasicek model with jump. The study was conducted by reconstructing the European put option pricing equation. The jump size is defined following a mixed-exponential distribution. By utilizing infinitesimal generators and martingale concepts, Laplace transform is constructed for the distribution of the Vasicek model with jump. Then, using the results of the Laplace transform for the distribution of the Vasicek model with jump and the concept of equivalent martingale measure, the European put option pricing equation with underlying asset zero-coupon bond is constructed.

Abstrak :
This book explains the philosophy of the polar encoding and decoding technique. Polar codes are one of the most recently discovered capacity-achieving channel codes. What sets them apart from other channel codes is the fact that polar codes are designed mathematically and their performance is mathematically proven. The book develops related fundamental concepts from information theory, such as entropy, mutual information, and channel capacity. It then explains the successive cancellation decoding logic and provides the necessary formulas, moving on to demonstrate the successive cancellation decoding operation with a tree structure. It also demonstrates the calculation of split channel capacities when polar codes are employed for binary erasure channels, and explains the mathematical formulation of successive cancellation decoding for polar codes. In closing, the book presents and proves the channel polarization theorem, before mathematically analyzing the performance of polar codes.